The applied analysis team, composed of 31 permanent members and about 30 PhD students, ATER and post-doctoral fellows, covers a very broad spectrum from theoretical analysis of PDEs and numerical analysis to modeling in connection with other disciplines. The activities of the applied analysis team can be divided into four main themes, which naturally have strong connections between them: analysis (functional analysis, analysis on varieties, geometric analysis and calculus of variations), PDEs with control and inverse problems, numerical analysis, and modeling in connection with other disciplines.

Many members of the team participate in several themes. Despite the wide range of research topics, a weekly “generalist” seminar brings together all the members. In parallel, 5 working groups, three of which are in collaboration with other teams or laboratories, operate on a regular basis and thematic days are organized on average twice a year. Each year, a meeting in Porquerolles brings together the majority of the team members over 3 days. Since 2012, it is done in collaboration with the mathematics laboratories of the universities of Nice and Toulon. Six members of the team are holders of national or international research contracts (ANR, GDR) and several of them are members of national and international research projects with Mexico, Maghreb, Spain, Taiwan. During this quadrennium, the members of the applied analysis team have published 366 articles and 4 books. They have been invited plenary speakers at more than 140 international conferences and have made more than 120 invitations to foreign universities. They have organized numerous international conferences, or national conferences like CANUM 2014, for example. In addition, 26 theses have been defended, including 2 in co-supervision, and 24 others are in progress. The dynamism of its members has resulted in 5 lecturers being promoted to professors during the period, 4 of whom are in another laboratory.

**Presentation of the team**

The Applied Analysis team is currently composed of 10 professors and one on secondment, 1 research director, 1 professor emeritus, 17 lecturers (and 2 on secondment), 4 post-doctoral students and 24 PhD students. We will welcome a new lecturer in September 2016.

– DR CNRS : Nicolaï NADIRASHVILI

– PR : Philippe ANGOT, Assia BENABDALLAH, Mihai BOSTAN, Yves DERMENJIAN (emeritus),

Thierry GALLOUËT, Olivier GUÈS, François HAMEL, Raphaèle HERBIN, Florence HUBERT (from 1/09/2016), Jacques LIANDRAT, Anne NOURI.

– MCF : Marie Thérèse AIMAR, Laure CARDOULIS, Guillemette CHAPUISAT, Michel CRISTOFOL, Julia CHARRIER, Emil ERNST, Christophe GOMEZ, Maxime HAURAY, Marie HENRY, Sylvie MONNIAUX, Morgan MORANCEY, Julien OLIVIER, Enea PARINI, Olivier POISSON, Kacem SAIKOUK, Pieralberto SICBALDI, Ali SILI (Univ. du Sud Toulon-Var), Magali TOURNUS,

– On secondment : Lorenzo BRASCO (MCF, “professore associato” at Università degli Studi di Ferrara, Italy since November 2015), Yannick SIRE (MCF, Full Professor with tenure at Johns Hopkins University, Baltimore, USA since July 2015), Philippe TCHAMITCHIAN (PR, director of the institutions section at AERES, then at HCERES, and now President of the Paris Est comue).

– Post-doctoral students (currently) :

– Wei-Jie SHENG (Chinese Scholarship Council, from 01/04/2016 to 31/03/2017, under the direction of F. Hamel),

– Diana WHITE (CDD CNRS on Pharmatubule project, from 01/01/2016 to 01/07/2016, under the supervision of F. Hubert).

– PhD students (currently) :

– Damien ALLONSIUS (normalien stipendiary, dir. F. Boyer and M. Morancey),

– Ayuna BARLUKOVA (Labex grant, directed by F. Hubert),

– Thomas BLANC (ministerial scholarship, directed by F. Boyer and M. Bostan),

– Julien BRASSEUR (ANR grant NONLOCAL project, cotutelle with the University of Milan, dir. J. Coville, F. Hamel, E. Valdinoci),

– Cécile CARRÈRE (allocatrice normalienne, directed by A. Benabdallah and G. Chapuisat),

– Benjamin CONTRI (ministerial scholarship, directed by G. Chapuisat and F. Hamel),

– Sophie DALLET (CIFRE scholarship, directed by J.M. Hérard),

– Sylvain DOTTI (employee, PRAG at the University of Reunion, directed by T. Gallouët and J. Vovelle),

– Aurélie FINOT (scholarship from the region, directed by M. Bostan and M. Hauray),

– Emilien GARCIA (CIFRE Exlog grant, directed by J. Liandrat),

– Marie-Ève GIL (ministerial scholarship, dir. H. Berestycki, F. Hamel and L. Roques),

– Pierre-Antoine GIORFI (doctoral student, IRFM scholarship, dir. A. Nouri and Ph. Ghendrih),

– Dyonisis GRAPSAS (dir. R. Herbin and J.-C. Latché),

– Hongjun GUO (China Scholarship Council grant, dir. F. Hamel),

– David IAMPETRO (CIFRE EDF grant, directed by J.M. Hérard),

– Zhiqing KUI (China Scholarship Council grant, directed by J. Liandrat),

– Hypolite LOCHON (CIFRE EDF scholarship, directed by J.M. Hérard),

– Sébastien MARMIN (cotutelle, IRSN scholarship, directed by J. Liandrat and D. Ginsbourger of the University of Bern),

– Laurent QUAGLIA (employee, high school teacher, dir. T. Gallouët),

– Giulio ROMANI (cotutelle, A*MIDEX Academy of Excellence Doctoral College scholarship, dir. F. Hamel, E. Parini, and B. Ruf of the University of Milan),

– Samir SALEM (ministerial scholarship, dir. M. Hauray),

– El Hadji Abdou SAMB (salaried, secondary school teacher, dir. A. Benabdallah),

– Juan Antonio SOLER (Amidex/Centrale Marseille scholarship, dir. J. Liandrat and E. Serre), – Abdelkader TAMI (dir. Ph. Tchamitchian),

– Rémi TESSON (recipient of a grant from the Ecole Normale Supérieure, directed by F. Hubert).

Movements: arrivals and departures since 2011

*Arrivals*

– Mihai BOSTAN (ITER), recruited PR in 2011,

– Lorenzo BRASCO (calculation of variations), recruited as MCF in 2011,

– Laure CARDOULIS (MCF) (inverse problems), arrived from Toulouse as MCF in the team in 2015 following a job exchange,

– Christophe GOMEZ (interaction edp-probabilities), recruited as MCF in 2012,

– Julia CHARRIER (numerical analysis-probabilities), recruited as MCF in 2012,

– Julien OLIVIER (complex fluid mechanics-modeling), recruited MCF in 2012, – Enea PARINI (calculus of variations), recruited MCF in 2012,

– Morgan MORANCEY (control), recruited as MCF in 2014,

– Magali TOURNUS (maths-bio), recruited as MCF in 2015.

– Loïc LE TREUST (non linear analysis of edp), recruited MCF in 2016

*Departures*

– Catherine CHOQUET, recruited PR in 2011 at the University of La Rochelle, – Claudia NEGULESCU, recruited PR in 2011 at the University of Toulouse 3, – Emmanuel RUSS, recruited PR in 2011 at the University of Grenoble-Alpes, – Patricia GAITAN, recruited PR in 2012 at AMU (CPT laboratory),

– Pierre BOUSQUET, recruited PR in 2014 at the University of Toulouse 3,

– Franck BOYER (PR) who transferred in 2015 to the university of Toulouse 3.

**Scientific report**

**Functional analysis, harmonic analysis, analysis on varieties, geometric analysis, calculus of variations**

Functional and harmonic analysis (P. Bousquet, S. Monniaux, E. Russ)

In a book, D. Mitrea, I. Mitrea, M. Mitrea and S. Monniaux are interested in situations in analysis in which one can construct a metric compatible with a given framework. In particular, they improve the theorem of Macias and Segovia of 1979 in the sense that the constants obtained are optimal. Many applications and examples are given. In particular, they show how the open application, closed graph and Banach-Steinhaus theorems can be extended to more general settings than that of complete metric spaces.

P. Auscher, S. Monniaux and P. Portal studied non autonomous Cauchy problems with operators in divergence form, using singular integrals on tent spaces (à la Coifman, Meyer, Stein).

M. Efendiev and E. Russ introduced Hardy spaces for the conjugate Beltrami equation in doubly related domains of the complex plane, and solved in these spaces the Dirichlet problem for the conjugate Beltrami equation, with Lp data on the edge, the real part of the solution being prescribed on one portion of the edge, its imaginary part on the other portion.

P. Bousquet studied critical cases for the divergence equation, Hardy inequalities for underdetermined systems, topological singularities in Sobolev spaces (density theorem for smooth functions in variety-valued Sobolev spaces), and the distributional Jacobian of variety-valued Sobolev applications.

Poincaré inequalities (E. Russ and Y. Sire)

C. Mouhot, E. Russ and Y. Sire have obtained L2 Poincaré inequalities in which the L2 norm of the gradient is replaced by a nonlocal quantity, for general μ-measures which satisfy a usual L2 Poincaré inequality. This result, obtained in the case of Rn , was extended by E. Russ and Y. Sire to the case of a Lie group with polynomial growth.

Stokes problem (S. Monniaux)

With A. McIntosh, S. Monniaux exploits a first-order formulation for the Stokes problem to obtain stronger results, and in more general domains, than those known so far and this in a larger variety of spaces. With T. ter Elst, she studies the “Dirichlet-to-Neumann” operator associated to the Stokes problem in order to find Friedlander-like estimates of the eigenvalues of the Stokes operator with Dirichlet and Neumann edge conditions.

Calculus of variations, optimization, convex analysis (P. Bousquet, L. Brasco, E. Ernst, E. Parini, P. Sicbaldi)

P. Bousquet, L. Brasco, G. Carlier and V. Julin have studied the lipschitz regularity for some elliptic equations with very large degeneracies, equations which are not much studied and which appear naturally in optimal transportation problems with congestion effects. They studied in particular equations with degeneracies confined in balls as well as anisotropic variants of the p-laplacian. P. Bousquet also analyzed the Lavrentiev phenomenon and the validity of the Euler-Lagrange equation.

E. Parini obtained results for quasi-linear equations of the p-laplacian type, with F. Charro. With N. Saintier, he also studied isoperimetric problems, related to spectral problems. E. Parini, B. Ruf and C. Tarsi have identified the optimal constants for a higher order functional inequality. F. Hamel, E. Parini and B. Ruf supervise the thesis of G. Romani on the positivity properties of the Kirchoff-Love functional, in cotutelle with the University of Milan and in the framework of a grant from the A*MIDEX Academy of Excellence.

E. Ernst gave a characterization of domains of definition which implies the automatic continuity of any convex function defined there, a problem posed in 1965 by D. Gale, V. Klee and T. Rockafellar. In collaboration with M. Volle, M. A. Lopez and N. Dinh, he discussed the convergence of augmented Lagrangian methods in multi-criteria optimization and two Hahn-Banach type theorems applied to optimization.

Spectral inequalities, rearrangement inequalities for linear and nonlinear problems (L. Brasco, F. Hamel, N. Nadirashvili, E. Russ)

L. Brasco, with G. De Philipps, A. Pratelli, B. Ruffini and B. Velichkov, showed the stability of the isoperimetric inequalities for the first Neumann eigenvalue, the second Dirichlet eigenvalue and the first Stek- lov eigenvalue, as well as the Bhattacharya-Nadirashvili-Weitsman conjecture concerning the stability of the Faber-Krahn inequality for the first Dirichlet eigenvalue. L. Brasco and G. Franzina have shown some isoperimetric in-equalities for the eigenvalues of the p-laplacian and its anisotropic versions, and have also given a new proof of the simplicity of the first Dirichlet eigenvalue of a nonlinear operator of the p-laplacian type.

L. Brasco and E. Parini, with E. Lindgren and M. Squassina, have studied the eigenvalue problem for the fractional p-laplacian, a non-local version of the classical p-laplacian, which is nothing else than the Euler-Lagrange equation for a Sobolev-Slobodeckii semi-norm. They studied the differentiability, for the super-quadratic case, of weak solutions of this nonlinear, nonlocal equation.

F. Hamel, N. Nadirashvili and E. Russ have shown Faber-Krahn type inequalities for the first eigenvalue of elliptic operators of order 2, nonsymmetric in general, on bounded domains of Rn with Dirichlet condition and under different geometric, integral or pointwise constraints on the parameters. They have introduced a new symmetrization method, different from the Schwarz method used for symmetric operators, and have shown new differential point inequalities. F. Hamel and E. Russ showed “Talenti-like” comparison results for elliptic problems with nonlinear dependence H(x,u,∇u) and at most quadratic on the terms in ∇u.

Analysis on varieties (N. Nadirashvili, P. Sicbaldi)

N. Nadirashvili studied metrics on Riemannian surfaces of given conformal type and unit area that maximize the nth eigenvalue of the Laplacian. He proved the existence of extremal metrics and characterized them in terms of the harmonic application of a given surface in the k-dimensional sphere. He gave a constructive proof of a critical metric which is regular outside a finite number of conic singularities and maximizes the first eigenvalue in the conformal class of the underlying metric. He proved the existence of an application associating to a point of the surface a family of eigenvectors corresponding to the maximized eigenvalue. He also gave new bounds on the number of negative eigenvalues of the Schrödinger operator.

In collaboration with E. Delay, J. Lamboley and F. Morabito, P. Sicbaldi studied the extremal domains, under volume constraint, for the first Laplace-Beltrami eigenvalue in Riemannian varieties, obtaining in particular results on the existence and localization of these domains, which depend on the curvature of the variety. He also generalized the study to the case of varieties with edge, where the curvature of the edge plays an important role. Finally, he studied the existence of non-trivial solutions to overdetermined elliptic problems in homogeneous varieties.

KAM theory, networks and Hamiltonian PDEs (Y. Sire)

R. de la Llave and Y. Sire studied the existence and qualitative properties of quasi-periodic solutions admitting hyperbolic directions. They have treated in particular the case of discrete networks and the case of ill-posed PDEs.

**Partial Differential Equations, Control and Inverse Problems**

Partial analyticity for hyperbolic or elliptic systems (N. Nadirashvili)

N. Nadirashvili and his collaborators have generalized results of S. Bernstein, H. Levy, I. Petrovsky and Morrey concerning solutions of nonlinear elliptic systems, analytic with respect to a group of variables, under assumptions of partial analytic dependence. He obtained several applications concerning the analyticity of solutions for 2D Euler and water waves without surface tension. For quasilinear wave equations he revisited a result of Alinhac and Métivier on the propagation of the partial analyticity of solutions, obtaining a more general and simpler proof.

Control and Inverse Problems (A. Benabdallah, F. Boyer, L. Cardoulis, M. Cristofol, Y. Dermenjian, M. Morancey, O. Poisson)

Within the Applied Analysis team, the Control and Inverse Problems group, which has been active for more than ten years, is composed of half a dozen permanent members who are joined by guests, post-doctoral fellows or PhD students. A monthly working group gathers its members.

The control theme is mainly studied by A. Benabdallah, F. Boyer (who moved to Toulouse since 2015), Y. Dermenjian and M. Morancey, and the inverse problem theme by L. Cardoulis, M. Cristofol and O. Poisson.

A. Benabdallah works on the observability of parabolic or elliptic operators with dis- continuous coefficients. With Y. Dermenjian and J. Le Rousseau she proved a Carleman inequality in the case of partially stratified operators, then with Y. Dermenjian and L. Thévenet she extended this inequality to the case of partially anisotropic elliptic operators. Moreover, she continued her research on the control of coupled parabolic equations. Together with F. Ammar Khodja, M. González-Burgos and L. de Teresa, she formulated necessary and sufficient conditions for controllability of classes of parabolic systems. Also with the same collaborators, she has highlighted completely new and counter-intuitive behaviors, qualified as hyperbolic phenomena (appearance of a strictly positive minimal control time, influence of the geometry). An article summarizing the results has been published, a book is being written and, with M. Morancey, an ANR project on the study of these hyperbolic phenomena in the control of parabolic equations has been submitted. On this subject, she is supervising the thesis of El Hadji Samb. With F. Boyer, M. González-Burgos and G. Olive, she obtained the first result of control by the edge of parabolic systems in space dimension > 1. With M. Cristofol, P. Gaitan and L. De Teresa, she proved an observability inequality for a parabolic system of 3 equations with space-dependent coefficients with observation of only one component.

M. Morancey studied the controllability of degenerate parabolic equations, in particular of Gru- shin type. On this problem, in collaboration with K. Beauchard and L. Miller, he characterized the minimal time required for controllability at zero. By considering in addition a singular potential, he proved the approximate controllability for adequate transmission conditions.

F. Boyer has contributed to the study of the exact or approximate controllability of equations or polar systems and/or their discretization. Among the outstanding results, we can note the identification of geometrical conditions on the control domain for the approximate controllability of coupled parabolic systems (in collaboration with G. Olive). He also continued the development of discrete Carleman estimates and their applications.

L. Cardoulis, who has just moved to the team in 2015, has worked on an inverse problem for the Schrödinger operator in an unbounded band with a stability result for two coefficients, one of which is time dependent, with P. Gaitan. The study of the reconstruction of the curvature of an unbounded waveguide has been done with M. Cristofol.

M. Cristofol treated the case of the reconstruction of coefficients for nonlinear parabolic operators with or without memory term and addressed the case of linear and nonlinear parabolic systems. In addition to the collaborations already mentioned, he used techniques from Carleman’s inequalities with P. Gaitan, K. Niinimaki, O. Poisson, L. Roques and M. Yamamoto. He has developed with L. Roques, in dimension one, a new approach based on minimal point-like observations in space for parabolic inverse problems. He worked on inverse problems of reconstruction of coefficients related to the Maxwell operator with M. Bellassoued, L. Beilina, K. Niinimaki and E. Soccorsi. He studied the case of an infinite hyperbolic waveguide with S. Li and E. Soccorsi and is currently interested in the generalization of this result to the case of time-dependent coefficient reconstruction with the numerical simulations of L. Beilina. He studied with M. Bellassoued the problem of final overdetermination for the reconstruction of a source in a parabolic system. He works, with L. Roques, on the reconstruction of the drift term in the general formulation of a diffusion problem and on the reconstruction of the volatility in a Black and Scholes type problem with M. Bellassoued, R. Brummelhuis and E. Soccorsi.

O. Poisson is working in collaboration with H. Isozaki on several inverse problem projects, including a first project on the spectral analysis of a Maxwell operator on a lattice and another on the reconstruction of a moving object for the wave operator. He has published a work which is an extension of results of Calderon’s problem for the heat equation with moving inclusion.

Homogenization, high frequency oscillations, singular perturbations (M. Bostan, O. Guès, A. Sili)

M. Bostan worked on the homogenization of transport equations. The multiscale analysis was based on the use of ergodic mean operators. This led, in particular, to a two-scale approach, with fast variable not necessarily periodic. These techniques have also allowed the treatment of parabolic problems with strongly anisotropic scattering and a theoretical study of the spectral properties of the averaged scattering matrix field. Some interesting results have been obtained in a nonlinear framework (Vlasov-Poisson system): strong convergence for not necessarily well prepared data, study of invariants, Hamiltonian structure of the limit model. This is the content of a thesis financed by the region, field of strategic activities. The perspectives aim at models with curved 3D confinement field, and the consideration of more realistic scaling laws (quasi-neutrality). Numerical simulation is also among the objectives.

A. Sili has continued his research work in this theme with various collaborators, leading to eight publications and the defense of Charef Hamid’s thesis (end of 2012).

O. Guès worked in collaboration with J.-F. Coulombel (univ. de Nantes) and M. Williams (Univ. North Carolina, USA) on the propagation and reflection of high frequency waves against a shock wave in multi-D (completing a previous work of M. Williams) under strong stability assumptions, then against an edge for weakly stable boundary conditions, highlighting the amplification of the wave, for semi-linear hyperbolic systems. These results were obtained thanks, among other things, to the precise study of a singular pseudodifferential calculation with small parameters, introduced in 2002 by M. Williams.

O. Guès, in collaboration with G. Métivier, M. Williams and K. Zumbrun, has been interested in the convergence and boundary layer problems posed by the low viscosity perturbation of a multidimensional hyperbolic system in the vicinity of a fixed edge and under a Neumann (or mixed Dirichlet-Neumann) condition, obtaining convergence in some favorable cases.

T. Auphan, in the framework of his thesis work, was interested in the theoretical problem of approaching a multidimensional symmetric hyperbolic quasilinear mixed problem of order 1, with dissipative boundary conditions by a fictitious domain volume penalization: he showed that there exist penalizations generating no spurious boundary layer at the interface, at any order, when the penalization parameter tends to 0, and he proved the convergence.

Mean field limits and kinetic models (M. Hauray, A. Nouri)

M. Hauray has worked on mean field limits and propagation for different models: 3D Vlasov equations with moderately singular interaction force, 1D Vlasov-Poisson equation with or without noise, swarm models (Vicsek), 2D Navier-Stokes equation approximated by vortex systems, 3D Landau equation with moderately soft potential. He has also been interested in stability problems of stationary profiles for plasmas in the quasi-neutral limit.

A. Nouri’s research activities are focused on applied mathematical problems modelled by kinetic equations:

– Tokamak core plasma where a Vlasov equation for the ion distribution function is coupled to the quasi-neutrality equation ;

– some quantum kinetic equations, such as the one modeling anyons;

– evolution of Bose-Einstein condensates, modeled by a Schrödinger equation of Gross-Pitaevskii type, in the middle of a gas of excitations, described by a quantum kinetic equation.

She collaborates with P. Ghendrih (IRFM of CEA Cadarache), P.-E. Jabin (University of Maryland) and C. Bardos on the study of tokamak core plasmas. With L. Arkeryd from Chalmers, Göteborg, she studies quantum kinetic equations, and with C. Schmeiser from Vienna she is interested in a chemotactic problem.

Fluid mechanics (T. Gallouët, S. Monniaux, N. Nadirashvili)

T. Gallouët continued his work on fluid mechanics problems, which led to 4 publications on the existence of solutions for elliptic problems, on the existence of solutions for compressible Stokes equations, and on the continuity in time of the entropic solution of an evolution problem (hyperbolic or degenerate parabolic).

S. Monniaux has been interested more particularly in the (linear) Stokes (or Stokes-Coriolis) system with different edge conditions in (bounded or not) lipschitzian domains. The good understanding of the properties of the linear problem allows to obtain, thanks to classical fixed point theorems, global solutions to the Navier-Stokes equations for small initial conditions. Contrary to the case of regular domains, the Stokes operator has very different properties from the vector Laplacian. She obtained elementary proofs of the existence of traces on the ∂Ω edge of functions in H1(Ω), and of integrable square u-vector fields whose divergence and rotationel are integrable square and which have a normal trace or zero tangential trace on the ∂Ω edge (one published conference proceedings and one report on these topics).

N. Nadirashvili proved that the only three-dimensional Beltrami flow of finite energy is trivial.

Propagation phenomena for reaction-diffusion type evolution PDEs (G. Chapuisat and F. Hamel)

Wave propagation phenomena are one of the most important aspects of reaction-diffusion models. W. Ding, J. Garnier, T. Giletti and F. Hamel, with H. Berestycki, M. El Smaily, J.-S. Guo, R. Huang, G. Nadin, J. Nolen, J.-M. Roquejoffre, L. Roques, L. Rossi, L. Ryzhik, Y. Sire, X. Zhao and A. Zla- toš, have studied the existence and qualitative properties of pulsating fronts in periodic media or generalized transition fronts, a notion introduced by H. Berestycki and F. Hamel unifying the known notions and constituting the natural mathematical framework for the study of space-time dynamics in complex heterogeneous media. Examples of propagation with multiple or infinite velocities have been highlighted. The thesis of H. Guo, under the supervision of F. Hamel, deals with the stability of transition fronts. Multiple research directions concern in particular problems with non-local dispersion or competition, work which is being done in the framework of the ANR NONLOCAL project.

G. Chapuisat in collaboration with H. Berestycki and J. Bouhours has studied the propagation of bistable fronts as a function of the geometry of the domain where they propagate.

Qualitative properties for local and non-local elliptic PDEs (T. Gallouët, F. Hamel, N. Na- dirashvili, P. Sicbaldi and Y. Sire)

F. Hamel, N. Nadirashvili and Y. Sire have constructed the first examples of positive solutions of semi-linear elliptic equations in convex domains with Dirichlet condition at the edge and having non-convex level sets, thus answering in the negative a conjecture of P.-L. Lions dating from 1981. M. Efendiev and F. Hamel have in particular used the dynamical systems approach to M. Efendiev and F. Hamel have used the dynamical systems approach to obtain results on the asymptotic behavior of solutions of elliptic equations in unbounded greens. Finally, one-dimensional symmetry results have been shown by D. Bonheure, F. Hamel, X. Ros-Oton, Y. Sire and E. Valdinoci for equations with non-local dispersion or for elliptic equations of order 4. The study of harmonic applications, dispersive effects and regularity theory has been analyzed by Y. Sire and his collaborators.

T. Gallouët has published two papers on existence results for elliptic problems.

P. Sicbaldi studied overdetermined elliptic problems in unbounded domains of Euclidean space. A very deep and surprising connection with minimal surfaces and surfaces with constant mean curvature allowed to find counterexamples to a Berestycki-Caffarelli-Nirenberg conjecture of 1997, and to reformulate the open questions for a possible classification. In particular, in the plane he obtained a general classification result for solutions on domains diffeomorphic to the half-plane. Work in collaboration with F. Schlenk, A. Ros and D. Ruiz.

**Numerical analysis**

Controllability of discretized parabolic problems (F. Boyer, F. Hubert)

Controllability results have been obtained for semi-discrete parabolic problems (in space) but also completely discretized in time and space. Time error estimates for the computation of the control on these problems have also been obtained. An essential tool underlying these results is the proof of discrete Carleman inequalities (F. Boyer, F. Hubert, collaboration with J. Le Rousseau).

Numerical methods for elliptic and parabolic equations (Ph. Angot, F. Boyer, T. Gal- louët, O. Guès, R. Herbin, F. Hubert, J. Liandrat)

Many works have been done for the development of the method called Discrete-Duality-Finite-Volume (DDFV), for example, for the development of the method for heterogeneous anisotropic operators (F. Hubert, N. Hartung, collaboration with B. Andreianov and Y. Coudière), in particular in 3 space dimensions, and for the Stokes problem (F. Boyer, F. Nabet, collaboration with S. Krell)

New discrete Schwarz methods have been proposed for Ventcell transmission conditions in the case of isotropic convection-diffusion operators (F. Hubert, in collaboration with L. Halpern) as well as in the case of anisotropic operators (F. Hubert in collaboration with L. Halpern, M. Gander, S. Krell) using DDFV methods.

A new numerical method, gathering different methods (non-conformal finite elements, gradient schemes, mimetic methods, gradient schemes, MPFA schemes…), called “Gradient Dis- cretization Method” (GDM) has been introduced for the discretization of elliptic and parabolic PDE. The interest of this method is to give a theoretical framework allowing the analysis of many schemes for linear and nonlinear PDEs, including for example a complete analysis of mass lumping. A book on MDM should be published soon (T. Gallouët, R. Herbin, collaboration with J. Dro- niou, R. Eymard, C. Guichard). Some of these schemes have been analyzed and implemented numerically for example for image processing or for flows in anisotropic heterogeneous porous media (R. Herbin, in collaboration with R. Eymard, K. Mikula, A. Handlovicova, O. Stavsovà, R. Masson, C. Guichard)

Methods coupling wavelets and dummy domains for the solution of elliptic problems in dimension 2 have been analyzed (J. Liandrat, in collaboration with P. Yin).

New methods have been developed for flow problems in porous media and for the analysis of interface and boundary layer conditions, possibly coupled with a free medium (Ph. Angot, C. Zaza, in collaboration with G. Carbou and V. Péron).

An asymptotic preserving method has been developed for nonlinear anisotropic elliptic problems appearing in tokamak modeling (Ph. Angot, T. Auphan, O. Guès).

In the context of tokamak modeling, a contribution to the penalization method for dealing with Robin-type boundary conditions has been made (J. Liandrat, in collaboration with G. Chiavassa and B. Bensiali).

High order numerical schemes have been developed for convection-diffusion equations. Their interest is to preserve the positivity of the approximated solutions on general meshes for convection and “admissible” for diffusion (R. Herbin, in collaboration with F. Babik, J.-C. Latché, B. Piar).

Nonlinear subdivision schemes (J. Liandrat)

Nonlinear subdivision schemes, obtained by nonlinear perturbation of linear schemes, have been introduced and analyzed (J. Liandrat, in collaboration with S. Amat and J. Ruiz). New schemes derived from stochastic prediction methods have been defined and analyzed (J. Liandrat, in collaboration with J. Baccou and X. Si).

Incompressible fluid mechanics (Ph. Angot, F. Boyer, T. Gallouët, R. Herbin)

Different methods for solving the incompressible Navier-Stokes equations have been introduced, splitting method, penalization method or a very original method of “vector” pressure correction (Ph. Angot, R. Cheaytou, collaborations with J.-P. Caltagirone, P. Fabrie, P. Minev). These methods are designed to be robust to large ratios of density, viscosity, permeability or open boundary conditions.

The stability of the Crank-Nicholson scheme with pressure correction has been shown (F. Boyer, F. Dar- dahlon, in collaboration with J.-C. Latché and C. Lapuerta).

Convergence results of the MAC scheme for incompressible Navier-Stokes equations (with possibly variable density) have been obtained (R. Herbin, T. Gallouët, K. Mallem, in collaboration with J.-C. Latché).

A numerical method for the solution of the 3-component Cahn-Hillard equation has been developed and analyzed (F. Boyer, S. Minjeaud)

Hyperbolic equations and systems (Ph. Angot, O. Guès, R. Herbin, M. Tournus)

A preserving asymptotic scheme has been developed for a hyperbolic system with a relaxation term (M. Tournus, in collaboration with N. Seguin).

In the context of tokamak modeling, a penalization method has been introduced and analyzed to deal with the boundary conditions problem (Ph. Angot, T. Auphan, O. Guès).

An error appearing in some papers on road traffic modeling has been highlighted and corrected (R. Herbin, in collaboration with L. Leclercq).

Transport equations (F. Boyer, T. Gallouët, R. Herbin)

The demonstration of the convergence of the upwind scheme for linear transport equations with an irregular transport field (DiPerna-Lions hypothesis) has been obtained, for the problem without boundary condition and with boundary condition (F. Boyer, A. Fettah, T. Gallouët, R. Herbin).

In the framework of a collaboration with the CEA, the development and the study of a numerical scheme for a system of transport equations have been carried out (D. Fournier, R. Herbin, in collaboration with R. LeTellier).

Compressible fluid mechanics (T. Gallouët, R. Herbin)

A proof of convergence of numerical schemes for stationary compressible Stokes equations has been given. It was then generalized for stationary or semi-stationary compressible Navier-Stokes equations. In the case of evolutionary Navier-Stokes equations, the adaptation of the so-called “strong-weak uniqueness” method has allowed to give error estimates between approximate solution and exact solution when the latter is sufficiently regular (T. Gallouët, R. Herbin, collaborations with R. Eymard, J.-C. Latché, D. Maltese, A. Novotny).

A series of works has been devoted to the study of new numerical schemes for the Euler or Navier-Stokes compressible type equations (barotropic or not, with possibly the addition of diffusion terms). These schemes do not use a Riemann solver and can be used at any Mach. The time discretizations can be implicit (with resolution by pressure correction) or partially implicit with a time step limitation depending only on the material velocities. Spatial discretizations use staggered or co-located meshes. An important originality of these methods consists in being able to discretize non-conservative equations (such as the internal energy equation) but keeping the correct velocities of the discontinuities. The good behavior of these methods is shown by numerical tests and by convergence demonstrations (consistency “in the sense of Lax”, R. Her- bin, W. Kheriji, J.-C. Latché, T.T. Nguyen, C. Zaza). A generalization to quasi-second order schemes has also been developed (R. Herbin, N. Therme, in collaboration with L. Gastaldo, J.-C. Latché).

Numerical methods have been developed and tested for the resolution of combustion models in multiphase media (D. Grapsas, R. Herbin, N. Therme, in collaboration with J.-C. Latché).

Stochastic PDE (J. Charrier, T. Gallouët)

Results have been obtained on the quantification of uncertainties for advection- diffusion problems (J. Charrier).

A series of works has been carried out on the convergence of numerical methods for the approximation of hyperbolic equations (in several space dimensions) with a stochastic source term of the “multiplicative noise” type (J. Charrier, T. Gallouët, C. Bauzet in the framework of a post-doctoral position).

**Modeling and interactions with other disciplines**

Interactions with physics (M. Bostan, Y. Dermenjian, C. Gomez, M. Hauray, J. Liandrat, J. Oli- vier, A. Nouri, K. Saikouk, M. Tournus)

M. Bostan has worked on the analysis of PDEs modeling tokamak plasmas: behavior in the presence of an intense stationary magnetic field (particles of disparate masses, treatment of col- lisions) or of a magnetic field strongly oscillating in time. A PhD thesis has been devoted to collisional gyro-kinetic models (relaxation, Fokker-Planck, Fokker-Planck-Landau). A second thesis is being finalized on the Vlasov-Poisson system in the finite Larmor radius regime. In parallel, he has obtained convergence results for parabolic problems with strongly anisotropic diffusion (thesis in progress, application to tokamak plasmas) and for population dynamics (swarming).

Y. Dermenjian studied guided waves of a biperiodic medium in an unbounded 3D domain, in collaboration with F. Bentosela, C. Bourrely and E. Soccorsi from CPT.

C. Gomez was interested in the phenomenon of wave propagation in random media with long-range correlations: with O. Pinaud, they provided a proof of the paraxial wave approximation with fractional white noise; with L. Ryzhik, they studied the radiative transport equation for which the collision kernel is singular (regularizing effect, scattering limits and peak forward).

In collaboration with C. Negulescu and R. Adami, M. Hauray worked on simplified models for the environment-induced quantum decoherence.

M. Hauray studied the Kac energy exchange model in dimension 1 and showed a uniform contractivity (in number of particles) in an adapted Wasserstein metric.

M. Hauray and A. Nouri studied the well-posedness of a quasi-neutral gyro-kinetic Vlasov equation in dimension 2: a model used in fusion plasmas, for example in the GYSELA code developed at CEA.

J. Liandrat works on the modeling of tokamaks. In particular, numerical simulations of particle tracking in a flow in the vicinity of walls, using interpolation techniques.

In particular, numerical simulations of particle tracking in a flow near walls, using interpolation techniques based on subdivision schemes have been carried out (in collaboration with P. Ghendrih and G. Ciraolo (CEA) and in the framework of the thesis of B. Bensiali).

In collaboration with P.-E. Jabin, A. Nouri has shown the well-posedness, local in time, in an analytical framework of a Vlasov equation coupled to the quasi-neutrality equation modeling the evolution of a tokamak plasma in the direction parallel to the magnetic field lines. With C. Bardos she showed that this system is ill-posed in the Hadamard sense in any Sobolev space.

A. Nouri works with L. Arkeryd on quantum kinetic equations. They have solved the Cauchy problem for an equation modeling anyons. They have also studied the interaction of Bose-Einstein condensates with a quasiparticle gas in a near equilibrium setting and determined the asymptotic behavior of such a system.

In collaboration with K. Martens, F. Puosi and E. Agoritsas (LiPhy – Grenoble), J. Olivier explored and tested the foundations of the mechanics of soft glassy materials. They have developed theoretical, numerical and physical tools to understand, compare and measure various behavioral scenarios in order to validate or invalidate certain theories.

K. Saikouk collaborates with J. Léchelle of the LLCC Laboratory of CEA Cadarache on the modeling and numerical simulation of nuclear fuel sintering. From a numerical point of view, this translates into the study of the evolution of interfaces between grains under mechanical and chemical effects.

M. Tournus is working with I. Aronson (Argonne National Laboratory, IL) and L. Berlyand (Penn State University, PA) on a model of an isolated microswimmer, in particular on the role of the flagellum in navigation and in collisions with solid walls.

Invasion models in ecology (F. Hamel, M. Henry)

J. Garnier, T. Giletti and F. Hamel, with O. Bonnefon, J. Coville, E. Klein and L. Roques, have studied the internal dynamics of biological invasion fronts for reaction-diffusion equations, which are well adapted to the description of certain ecological phenomena of colonization and dispersal of plants or animals. In particular, they have shown the positive role of the Allee effect on the preservation of diversity during a colonization. H. Berestycki, F. Hamel and L. Roques are supervising the thesis of M.-E. Gil on selection-mutation models in population genetics, in the framework of the ANR NONLOCAL project.

M. Henry is interested in traveling waves associated with reaction-diffusion systems, in the formation of interfaces and spatio-temporal patterns and in the dynamics of these interfaces.

Models in oncology (A. Benabdallah, G. Chapuisat, C. Gomez, F. Hamel, F. Hubert, J. Olivier, M. Tournus)

A. Benabdallah and F. Hubert have been working since 2007 on the modeling of the metastatic process. In collaboration with D. Barbolosi, they have supervised two theses (F. Verga and S. Benzekry) on the modeling of the impact of anti-cancer drugs on this progression using transport type equations. M. Henry and A. Benabdallah studied a viscosity approximation of these models. Still in collaboration with D. Barbolosi’s group, at the Center of Oncobiology and Oncopharmacology (CRO2), F. Hubert proposed a preclinical validation of the metastasis model (thesis of N. Hartung co-directed by G. Chapuisat and F. Hubert). This project was supported by the ANR (ANR MEMOREX) and the 2009-2013 Cancer Plan.

N. Hartung and F. Hubert collaborated with the team of Pr J. J. Grob’s team on the identification of efficacy indicators of anti-BRAF treatments in metastatic melanoma.

In an AMIDEX NOVUSBIO project led by E. Francescini of the Mechanics and Acoustics Laboratory, G. Chapuisat, N. Hartung and F. Hubert have started a work on the modeling of tumor growth in mice based on observations from SPECT and ultrasound imaging. N. Har- tung and F. Hubert proposed an algorithm, based on DDFV, to detect the contours of observed tumors.

Since 2013, F. Hubert and C. Gomez have been working, in collaboration with S. Honoré’s group (CRO2), on the dynamic instabilities of microtubules that result in alternating phases of poly- merization and depolymerization. They have obtained the support of A*MIDEX and the 2013-2017 Cancer Plan (PHARMATOTUBULE project). A. Barlukova in her thesis funded by LABEX ARCHIMEDE and supervised by F. Hubert and S. Honoré, uses deterministic models, discretized by finite vo- lumes techniques to account for the complexity of these dynamics and the actions of anti-microtubule chemotherapies. C. Gomez uses a stochastic approach to model this phenomenon. F. Hubert in collaboration with M. Tournus and D. White, post-doctoral fellow recruited on the project, proposed a new approach to depolymerization based on fragmentation equations.

In another context, this same fragmentation equation has been studied by M. Tournus in collaboration with M. Doumic (INRIA Roquencourt) and M. Escobedo (UPV). They are interested in the estimation (inverse problem) of the kernel and the fragmentation rate. A collaboration is in progress with W.F. Xue (School of Bioscience, UK) to apply their method to real data of proteins involved in neurodegenerative diseases.

In collaboration with O. Theodoly from the Adhesion and Diffusion laboratory in Marseille, F. Hubert and J. Olivier proposed at CEMRACS 2015 a study of cell migration in confined environments.

In the framework of C. Carrère’s thesis, A. Benabdallah and G. Chapuisat are working on the modeling of the growth of a heterogeneous tumor composed of chemotherapy resistant or sensitive cells from M. Carré’s in vitro experiments (CRO2). The optimization of chemotherapy leads to a complex optimal control problem.

Under the supervision of G. Chapuisat and F. Hamel, B. Contri studies medical models of spatial growth under the effect of periodic treatments.

**Academic influence and attractiveness**

**Networks and institutional contracts**

Members of the team are involved in many national and international projects.

– Projects led by members of the team

– ANR Blanc ANR-09-BLAN-0217-01 “MEtastases MOdeling and Reseach in EXperimental PharmacoKinetics” ( 2012-2013), coordinator : F. Hubert, I2M members : A. Benabdallah, G. Chapuisat,

– INSERM cancer plan 2009-2013, coordinator: F. Hubert, I2M members: A. Benabdallah, G. Chapuisat, N. Hartung,

– ANRNONLOCAL (ANR-14-CE25-0013) “Défi de tous les savoirs”,2014-2018. Coordinator: F. Hamel, I2M members: J. Brasseur, C. Carrère, G. Chapuisat, B. Contri, W. Ding, M.-E. Gil, H. Guo, F. Hamel, N. Nadirashvili and Y. Sire,

– INSERM PharMathTubules project, collaboration between CRO2 and I2M laboratories, 2013-2017, coordinator : F. Hubert, I2M members : A. Barlukova, C. Gomez, R. Tesson, D. White,

– PHC Tassili-2011no24296TE/11MDU834(2011-2014), coordinator: A.Benabdallah, I2M members: M. Cristofol, F. Boyer, Y. Dermenjian, P. Gaitan, F. Hubert and O. Poisson.

– Projects in which members of the team are involved

– ANR Blanc PREFERED (2008-2012), coordinator : J.-M. Roquejoffre (Toulouse), I2M members: F. Hamel, N. Nadirashvili, E. Russ and Y. Sire,

– ANR Blanc VFSitCom (2008-2012), coordinator: J.Droniou, I2M members:F.Boyer,R.Her-

bin and F. Hubert,

– ANR EMAQS (2012-2016) coordinator: K. Beauchard, I2M member: M. Morancey,

– ANR Geometrya (2013-2017), coordinator : H. Pajot, I2M member : P. Sicbaldi,

– ANR Harmonic Analysis at its Boundaries, coordinator : P. Auscher, I2M member : S. Monniaux,

– ANR INFAMIE, coordinator : R. Danchin, I2M member: S. Monniaux,

– ANR-08-BLANC-0335 CAGE (2009-2012), coordinator: F. Pacard (Créteil), I2M member: P. Sicbaldi,

– AMIDEX PHARMATOTUBULE, collaboration between CRO2 and I2M (2013-2015), coordinator: S. Honoré, I2M members: A. Barlukova, C. Gomez, F. Hubert, R. Tesson and D. White,

– GDR MOMAS (Mathematical Modeling and Numerical Simulations related to nuclear waste management problems) (2007-2012), coordinator: A. Ern (ENPC), I2M members: F. Boyer, T. Gallouët, G. Henry, R. Herbin and F. Hubert,

– GDR EGRIN (Modeling and numerical simulations Gravity flows and Natural Risks) (2015-2019), coordinator: C. Lucas, I2M members: Ph. Angot, T. Gallouët and R. Herbin,

– GDR MANU (Mathematics for nuclear energy) (2015-2019), coordinator: C. Cancès, I2M members: T. Gallouët, R. Herbin and F. Hubert,

– GDR CATIA (Control and Analysis of PDEs, Theory, Interactions and Applications) (2014-2018), coordinator: K. Beauchard, I2M members: A. Benabdallah, F. Boyer, M. Cristofol, Y. Dermenjian, P. Gaitan, F. Hubert, M. Morancey and O. Poisson,

– ERC ReaDi (ERC Grant Agreement n.321186), 2013-2017, coordinator: H.Berestycki, I2M members: G. Chapuisat and F. Hamel,

– GDRE Geometric Analysis (France-Spain), coordinators: P. Romon (Marne-la-Vallée) and J. Perez (University of Granada, Spain), I2M member: P. Sicbaldi,

– GDRE CONEDP (2009-2017), coordinator: F. Alabau, I2M members: A. Benabdallah, F. Boyer, M. Cristofol, Y. Dermenjian, P. Gaitan, F. Hubert, M. Morancey and O. Poisson,

– Analysis and control of PDEs with origin in physics and other sciences (2010-2014) (MTM2010- 15592), funded by the Spanish Ministry of Science and Innovation, coordinator: E.F. Cara, I2M member: A. Benabdallah,

– Franco-Brazilian research project SURFACES, ANR-11-IS01-0002 (2012-2015), coordinator: L. Hauswirth (Marne-la-Vallée), I2M member: P. Sicbaldi,

– GDRI Euro-maghrebian of mathematics and their interactions (2014-2018), coordinator: G. Lebeau, I2M members: A. Benabdallah, Y. Dermenjian and A. Sili,

– GDRI ReaDiNet (Korea-France-Japan-Taiwan,2014-2018), coordinator: D.Hilhorst, I2M members: G. Chapuisat, F. Hamel and M. Henry,

– LIA LAISLA (French-Mexican, 2009-2016), coordinators: H. Short and J. Seade, I2M members of the applied analysis team: A. Benabdallah.

**Scientific responsibilities**

Many members of the Applied Analysis team are involved in the collective tasks of organizing the research. In particular:

– A. Benabdallah is in charge of the AA team since September 2015 and a member of the I2M office.

– R. Herbin is the director of the I2M laboratory since July 2015 and was the AA team leader from 2012 to 2015.

– F. Hamel is director of the LabEx Archimède since 2014 (ANR-11-LABX-0033, this Labex gathers 5 units in mathematics and computer science). He was in charge of the ex-LATP at the ex-University of Aix- Marseille III until 2011.

– O. Guès was co-director of the mathematics department from 2012 to 2014.

– J. Liandrat was Director of Research (VP Scientific Council) at Centrale Marseille from 2010 to March 2016.

– M. Cristofol is a member of the research commission of the IUT of Aix-Marseille.

– F. Boyer and A. Nouri have been members of the UFR sciences board since 2012, F. Boyer was a member of the department board office from 2012 to 2015, and M. Bostan has been a member of the mathematics department board since November 2012 and the office since September 2015.

**Expertise**

Many members of the team have performed expert activities for various research bodies. Among them, we can mention :

– F. Hamel is or has been an expert, depending on the case, for the ANR, BIRS (Canada), ECOS-Sud (Chile), the ERC, Fondecyt (Chile), NSERC (Canada), RGC (Hong-Kong), for the research investment grant at the Université Pierre et Marie Curie, for international bilateral PICS projects in the fields of EDP and Scientific Computing. He was a member of the national commission in charge of the evaluation of the applications to the P.E.S. in mathematics in 2011 and 2012 and he was referent of the mathematics-computing disciplinary field for the COS of the University of Aix-Marseille in 2015.

– G.Chapuis is a member of the “Mathematics, Bioinformatics, Artificial Intelligence” Specialized Scientific Commission of INRA since 2015.

– R. Herbin was a member of the HCERES committee for the expertise of the IMB (Institut de Mathématiques de Bordeaux) in 2015, and of the AERES committee for the expertise of IRSTEA (ex-Cemagref) in 2013, and a member of several project evaluation committees (Germany, Spain, Czech Republic). She is also a member of the teaching commission of the SMAI.

– F. Hubert was a member of the ANR committee in 2012 and 2013. She is in charge of the scientific calculation option of the Aggregation of Mathematics, she has been a member of the scientific council of the GDR METICE since 2016 and was elected in 2015, vice-president of the SMAI in charge of communication and public actions.

– Cristofol has been an appointed member of CNU 26 since November 2015.

– M. Bostan has been a member of the AMU thesis commission since June 2013, of the board of the of the AMU-Entreprise development council and is a corresponding member of the Pôle des Recherches Intersectoral and Interdisciplinary Research Cluster (PR2I) – Energy, since September 2013.

Many members of the team participate each year in selection committees for positions AMU and outside AMU.

**Editorial Boards**

Members of the Applied Analysis team serve on editorial boards of journals including: Computational and Applied Mathematics, International Journal of Finite Volumes and ESAIM Proc., SIAM Journal On Uncertainty Quantification, Boletin de la Sociedad Matemática Mexicana, Kinetic and related Models, Taiwanese Journal of Mathematics, Tamkang Journal of Mathematics (since 2013)…

**Organization of scientific events**

Members of the team are involved in the organization of many international conferences including the following:

– In the context of the FVCA6 conference, R. Herbin and F. Hubert participated in the organization of a 3D performance evaluation on approximations of diffusion problems on general meshes (3D Benchmark on Discretization Schemes for Anisotropic Diffusion Problems on Gene- ral Grids, R. Eymard, G. Henry, R. Herbin, F. Hubert, R. Klofkorn and G. Manzini, Proceedings of Finite Volumes for Complex Applications VI, Praha, p.895 -930, 2011).

– Conference “Kinetic equations” in November 2014 at CIRM, organized by M. Bostan, M. Hauray and A. Nouri.

– Organized several international conferences at CIRM including: Current challenges of mathematics in cancer medicine and biology: modeling and mathematical analysis, Control, New challenges of mathematics in oncology and cancer biology, etc.

– Organization of the international colloquium of LE2MI, GDRI Euro-Maghreb of mathematics and their interactions, which is an international research grouping associated with the CNRS, which includes more than thirty-five laboratories from the Maghreb and France.

– Conference “Fronts and Nonlinear PDEs” in honor of H. Berestycki, Ecole Normale Supé- rieure, Paris, June 20-24, 2011 (about 200 participants) of which F. Hamel was one of the organizers.

– Conference “France-Taiwan Joint Conference on Nonlinear Partial Differential Equations”, Tai- pei, Taiwan, October 21-25, 2013, organizers: H. Berestycki, J.-S. Guo, F. Hamel, C.-S. Lin, B. Perthame and H.-T. Yau.

– Organization of Canum 2014 (http ://smai.emath.fr/canum2014/).

– Conference on Waveguides 2016, Porquerolles, May 17-19, 2016, organizers A.-S. Bonnet- Bendhia, Ph. Briet, M. Cristofol and E. Soccorsi.

– Conference “Reaction-Diffusion Equations and Applications”, Renmin University, Beijing, China, May 26-29, 2016, organizers: S. Cantrell, F. Hamel, Y. Lou, F. Lutscher and E. Yanagida.

Thematic days and mini-colloques are organized at a rate of two or three per year:

– Around kinetic problems (June 2011, talks by N. Crouseilles, T. Goudon, J. Barré).

– Analysis day (November 2011, mini-course by L. Saint-Raymond and A. Chambolle).

– Computation of Variations Day (December 2011, lectures by F. Santambrogio, G. de Philippis, Y. Sire and A. Blanchet).

– Optimal transport and applications in analysis and DPE and numerical schemes Asymptotic Preserving for Multiscale Kinetic Equations (May 2012, mini-course by F. Bolley and M. Lemou).

– Microscopic and macroscopic modeling of crowd movements and Multiscale modeling for hydrology and erosion models (October 2012, mini-course by B. Maury and S. Cordier).

– Recent progress in Nonlinear Analysis (December 2012, mini-course by B. Ruf and T. Weth).

– Hyperbolic models for fluids and numerical schemes (December 2013, two-day colloquium day symposium, lectures by A. Novotny, D. Doyen, S. Gavrilyuk, J. Sainte-Marie, A. Beccantini, M. H. Vignal, C. Berthon, S. Minjeaud, N. Seguin, and posters by T. Auphan, R. Cheaytou, D. Maltese, F. Nabet, N. Therme, C. Zaza).

– Colloquium Inverse problems and control in the framework of the GOMS working group (November 2014, presentations by M. Bellassoued, E. Bonnetier, D. Dos Santos Ferreira, J. Garnier, H. Isozaki, M. Mo- rancey, A. Munch, M. Yamamoto).

– Thematic days on stochastic conservation laws: theory, numerical analysis and applications (June 2015, talks by S. Boyaval, J. Charrier, A. Debussche, G. Vallet, J. Vovelle, P. Wittbold and A. Zimmermann).

– Optimization and control (December 2014, presentations by M.Caponigro, C.Laurent, P.Lissy, F.Rossi).

– Stability of periodic solutions for nonlinear equations (March2015, talks by S.Benzoni, F. Chardard, P. Noble, M. Rodrigues).

– Colloquium Inverse problems and associated domains in the framework of the GOMS working group (december 2015, presentations by G. Alberti, L. Oksanen, F. Triki, M. Yamamoto)

– Modeling: Mathematics and Realities (March 2016, presentations by A. Barberousse, J. Bouhours, C. Carrère, P. Gabriel, F. Givors, R. Tesson).

Thematic meetings of applied analysis, http ://champion.univ-tln.fr/NTM/NTM2016.html, now common with the AA teams of the mathematics laboratories of Nice and Toulon, are organized every year. For example, in June 2013, there were talks by T. Auphan, J. Charrier, D. Clamond, A. Dragoul, M. Ersoy, R. Eymard, D. Esslé, I. Lucardedi, S. Minjeaud, E. Parini, M. Ribot, J. Shneider and F.Sueur.

Moreover, in 2015, F. Hubert and J. Olivier supervised a project at CEMRACS, funded by the Pharmatotubules project.

**Awards**

– N. Nadirashvili was awarded the Gay-Lussac Humboldt Prize (Académie des Sciences) in 2013,

– J. Garnier received the 2012 thesis prize of the University of Aix-Marseille (thesis directors: F. Hamel and L. Roques),

– F. Hamel was a junior member of the Institut Universitaire de France from 2009 to 2014,

– F. Hamel was included in the list of “Highly Cited Researchers” (Thomson Reuters) in 2014,

– G. Romani is a laureate of the “Académie d’Excellence Collège Doctoral” program of A*MIDEX (thesis 2014-2017, co-directed by F. Hamel, E. Parini and B. Ruf in co-supervision with the University of Milan),

– F. Boyer is a junior member of the Institut Universitaire de France since 2016.

**Invited lectures in international conferences** (since 2011)

Team members have given more than 100 invited talks, of which the top 2 per person are:

— [INV(AA)] A. Benabdallah : Modelling and Control of Nonlinear Evolution Equations, Sissa, Trieste, 2011,

— [INV(AA)] A. Benabdallah : Conference “Mathematical Control” in Trieste, 2013,

— [INV(AA)] M. Bostan : Cemracs Numerical modelling of plasmas CRM, Marseille, 2014,

— [INV(AA)] M. Bostan : Numerical Methods for the Kinetic Equations of Plasma Physics (NumKin2015), Garching, Max-Planck-Institut for Plasma physics, 2015,

— [INV(AA)] F. Boyer : First French-Mexican Symposium on Industrial and Applied Mathematics, Villahermosa, Mexico, 2013,

— [INV(AA)]F.Boyer:French-Chinese conference on Industrial and Applied Mathematics, Xiamen, China, 2014.

— [INV(AA)] P. Bousquet : 12ème Colloque Franco-Roumain de Mathématiques Appliquées, Lyon, 2014,

— [INV(AA)] P. Bousquet : Optimization Days, an international workshop on Calculus of Variations, Università Politecnica delle Marche, Ancone, 2011,

— [INV(AA)]L.Brasco:”Non linear partial differential equations and stochastic methods”, Jyvaskyla (Finland), 2014,

— [INV(AA)] L. Brasco : “3rd Italian-Japanese Workshop on Geometric Properties for Parabolic and Elliptic PDE’s”, Tokyo Institute of Technology, Tokyo, 2013,

— [INV(AA)] G. Chapuisat : 12ème Colloque Franco-Roumain de Mathématiques Appliquées, Lyon, 2014,

— [INV(AA)] J. Charrier : NASPDE 2013 à Rennes, 2013.

— [INV(AA)] J. Charrier : Advances in Numerical Methods for SPDEs à l’institut Mittag-Leffler, Sweden, 2015,

— [INV(AA)] M. Cristofol : First Joint International Meeting RSME-SCM-SEMA-SIMAI-UMI, Bilbao, 2014,

— [INV(AA)] M. Cristofol : Mathematical Paradigms of Climate Science, Rome, Université de la Sapienza, Italie, 2013,

— [INV(AA)] Y. Dermenjian : “Mathematical Physics, Spectral Theory and Stochastic Analysis”, Goslar (Germany), 2011,

— [INV(AA)] Y. Dermenjian : “Recent development in inverse problems for partial differential equations and its applications”, Kyoto (RIMS), 2016,

— [INV(AA)] E. Ernst : ALEL2014, Sevilla, Spain, 2014,

— [INV(AA)] E. Ernst : OVA7, Alicante, Spain, 2016,

— [INV(AA)] P. Gaitan : Inverse Days 2011, University of Helsinki, Finland, 2011,

— [INV(AA)] P. Gaitan : International Conference on Inverse Problems (ICIP’14), University of Tapei, Taiwan, 2014,

— [INV(AA)] C. Gomez : Workshop Probability and PDEs, Pisa, Italia, 2013,

— [INV(AA)] C. Gomez : Workshop Interplay of Theory and Numerics for Deterministic and Stochastic Homogenization, Oberwolfach, Germany, 2013.

— [INV(AA)] F. Hamel : Second Sino-Chilean Conference on Nonlinear Elliptic and Parabolic PDE, Santiago, Chili, 2012,

— [INV(AA)] F. Hamel : Conférence “Qualitative and geometric aspects of elliptic PDEs”, CRM, Barcelona, Spain, 2013,

— [INV(AA)] M. Hauray : Workshop “Scaling Limits and effective theories in classical and quantum mechanics”, Erwin Schrödinger Institute, Vienna, 2014,

— [INV(AA)] M. Hauray : Conference “Perspectives in Analysis and Probability” pour l’ouverture du Centre Lebesgue, Rennes, 2013,

— [INV(AA)] R. Herbin : MAMERN, Pau, 2015,

— [INV(AA)] R. Herbin : Multiphase flow in industrial and environmental engineering AMIS, Chambéry, 2012,

— [INV(AA)] F. Hubert : Mini-symposium, French-Mexican Meeting on Industrial and Applied Mathematics, Villahermosa, Mexico, 2013,

— [INV(AA)] F. Hubert : 16ème Ecole Franco-Espagnole de simulation numérique, 2014,

— [INV(AA)] J. Liandrat : Curve and Surface fitting, Oslo, 2012,

— [INV(AA)] J. Liandrat : ICIAM 2015, Mini-symposium “Non linear subdivision schemes and applications”, Beijing 2015,

— [INV(AA)] S. Monniaux : “Recent Advances in Hydrodynamics”, BIRS, Banff, 2016,

— [INV(AA)] S. Monniaux : Workshop “Geophysical Fluid Dynamics”, MFO (Oberwolfach), 2013,

— [INV(AA)] M. Morancey : SIAM Conference on Control and its Applications, mini-symposium Analysis and Control of Hypoelliptic Diffusion, Maison de la Mutualité, Paris, 2015,

— [INV(AA)] M. Morancey : Control of partial differential equations, GSSI, L’Aquila, Italia, 2015,

— [INV(AA)] A. Nouri : “Advances in kinetic and fluid dynamics transport : Analysis and approximations”, Austin, 2016,

— [INV(AA)] A. Nouri : “Spectral and scattering theories in Quantum Field Theory”, Porquerolles, France, 2016,

— [INV(AA)] E. Parini : Cologne Conference on Nonlinear Differential Equations, Cologne (Germany), 2013,

— [INV(AA)] E. Russ : Rencontres d’analyse, Université de Louvain-la-Neuve, Belgique, 2011,

— [INV(AA)] E. Russ : Session du congrès IWOTA 2011, Séville, Espagne, 2011,

— [INV(AA)] P. Sicbaldi: Minimal surfaces,over determinated problems and geometric analysis, Santiago del Chile, (Chile), 2015,

— [INV(AA)] P. Sicbaldi : Surface theory, Sevilla (Spain), 2011,

— [INV(AA)] A. Sili : Tam-Tam Tanger, 2015,

— [INV(AA)] A. Sili : Third Workshop on Thin Structures, Napoli, 2013,

— [INV(AA)] Y. Sire : “Rutgers Geometric Analysis Conference”, Rutgers Univ., USA, 2015,

— [INV(AA)] Y. Sire : Congress ICIAM 2011, Vancouver, Canada, 2011,

— [INV(AA)] M. Tournus : AIMS, Orlando, USA, 2016.

**International collaborations**

Visits to foreign universities

The Applied Analysis team has a strong international influence. Its members make numerous visits abroad. Here is a non-exhaustive list of these visits:

– A. Benabdallah : University of Seville, Spain (1 week in 2011), University of Tokyo, Japan (10 days in 2014), University of Madrid (1 week in 2012), University Houari Boumédiène, Alger, Algeria (1 week in 2014, 2013, 2011),

– M. Bostan: Centre de Recerca Matemàtica, Universitat Autònoma de Barcelona (1 week in 2012), J. Tinsley Oden Fellowship, Institute for Computational Engineering and Sciences ICES, University of Texas at Austin (1 month in 2012), Imperial College London (1 week in 2015)

– J. Charrier: Bath, UK (1 week in 2014),

– M. Cristofol: University of Tokyo (2016, 2013, 2012, 2011), University of Science and Technology of China (USTC) (2015, 2014), University of Chalmers, Sweden (2014), University of Milan, Italy ( 2012), University of Algiers USTHB, Algeria (2012), Fundan University, China (2011),

– Y. Dermenjian: University of Tokyo (1 February to 3 March 2014 and 4 to 31 January 2016),

– P. Gaitan: Fudan and Nanjing Universities, China (10 days in 2012), University of Tokyo (10 days in 2013, 15 in 2014 and 10 in 2016),

– C. Gomez: Colorado State University (2 weeks in 2016), UC Irvine (1 week in 2016) and Stanford University (1 week in 2016),

– F. Hamel: University of Wisconsin, Madison and University of Iowa, Iowa City, USA (1 week in 2011), Memorial University Newfoundland, Canada (1 week in 2011), Stanford University, USA (1 week in 2011), Università Roma II Tor Vergata, Italy (1 week in 2011), Instituto Superior Tecnico, Lisbon, Portugal (1 week in 2011), University of Bath, UK (1 week in 2011), The Chinese University of Hong Kong (1 week in 2012), Université Libre de Bruxelles, Belgium (1 week in 2012), The University of California, Berkeley, and Stanford University, USA (6 months in 2013, visiting scholar and visiting professor), University of Toronto, Canada (1 week in 2013), University of Wisconsin and University of Chicago, USA (1 week in 2013), University of Padova, Italy (1 week in 2014), Memorial University Newfoundland, Canada (1 week in 2014), University of British Columbia, Canada (1 week in 2014), Université Libre de Bruxelles, Belgium (1 week in 2014), Weierstraß Institut, Berlin, Germany (1 week in 2015), University of Padua, Italy (1 week in 2015), University of Granada, Spain (1 week in 2016),

– R. Herbin: Essen Universitat (2011), University of Manchester (2015),

– J. Liandrat: University of Cartagena (2 weeks in 2013 and 2014),

– S. Monniaux: Australian National University in Canberra (Australia) in the framework of the LIA “Analyse and Geometry” (8 months in 2015), ICMAT Madrid (2 weeks in 2013), Temple University, Philadelphia, USA (2 weeks in 2012), University of Missouri-Columbia, USA (2012: 3 weeks), Visiting Professor at Technische Universität Darmstadt, Germany (6 months in 2011- 2012), ANU, Canberra (6 weeks in 2011),

– P. Sicbaldi: University of Granada (Spain) (6 months in 2012-2013, 6 months in 2013-2014 and 6 months in 2014-2015),

– Y. Sire: more than 40 stays, e.g. at Stanford, Princeton, Lausanne, Madrid, etc.

– M. Tournus: Rutgers University, USA (1 week in 2016).

Scientific collaborations abroad (with co-publications)

– University of Seville (M. Gonzalez Burgos, with A. Benabdallah),

– Autonomous University of Mexico (L. de Teresa, with A. Benabdallah),

– Université Houari Boumédiène d’Alger, (D. Téniou with M. Cristofol),

– University of Tokyo (M. Yamamoto, with A. Benabdallah, M. Cristofol, Y. Dermenjian), – Colorado State University, USA (O. Pinaud with C. Gomez),

– UC Irvine, USA (K. Sølna, with C. Gomez),

– Duke University (J. Nolen, with F. Hamel),

– Helmholtz Center Münich, Germany (M. Efendiev, with F. Hamel),

– Memorial University Newfoundland, Canada (X. Zhao, with F. Hamel),

– South China Normal University, China (R. Huang, with F. Hamel),

– Stanford University, USA (L. Ryzhik, with C. Gomez and F. Hamel),

– Tamkang University, Taiwan (J.-S. Guo, with F. Hamel),

– American University of Beirut, Lebanon (M. El Smaily, with F. Hamel),

– University of Padua (L. Rossi, with F. Hamel),

– University of Texas at Austin, USA (X. Ros-Oton, with F. Hamel),

– University of New England, Australia (W. Ding, with F. Hamel),

– University of Wisconsin, Madison, USA (A. Zlatoš, with F. Hamel),

– WIAS, Berlin, Germany (E. Valdinoci, with F. Hamel)

– Imperial College (J.A. Carrillo, formerly at UAM, Madrid, with M. Hauray),

– University of Milan Biccocca (R. Adami, with M. Hauray),

– University of Maryland (P.E. Jabin, with M. Hauray),

– T.U. Munich (Y.P. Choi, with M. Hauray),

– University of Geneva, Switzerland (M.J. Gander, with F. Hubert),

– Argonne National Laboratory, IL (I. Aronson, with M. Tournus),

– Penn State University, PA (L. Berlyand, with M. Tournus).

**Interaction with the socio-economic and cultural environment **

**Interaction with the industrial and socio-economic fabric**

At the regional level, there are strong links between the AA team and the Cadarache centre, CEA and IRSN.

A collaboration of more than 15 years exists between several members of the team and Jean-Claude Latché, senior expert at IRSN Cadarache, concerning the numerical simulation of severe accidents in nuclear power plants.

This work was carried out in particular by the co-direction between R. Herbin, L. Gastaldo (Fire and Explosion Laboratory) and J.-C. Latché of five theses, the last two focusing more specifically on the risk of hydrogen explosion, following the Fukushima accident in 2011. The algorithms developed in the context of these theses are implemented in the IRSN’s Calif3s code used for nuclear safety calculations.

The ITER project is the subject of joint work between CEA researchers:

– Supervision of Aurélie Finot’s thesis (November 2013 – October 2016) by M. Bostan and M. Hauray, funded by the PACA Region and for which CEA Cadarache is the socio-economic partner,

– A. A. Nouri is collaborating with Philippe Ghendrih of the IRFM in Cadarache on the study of plasmas in the tokamak core,

At the regional level, the Math-Medicine group has intensified its collaborations in recent years with pharmacologists or doctors from the CRO2 laboratory (Centre de recherche en oncobiologie et oncopharmacologie). Other collaborations with biologists, physicists or clinicians have emerged thanks to the meetings of the Cancéropole PACA. These collaborations have resulted in funding from the ANR, AMIDEX and the cancer plan.

We can also mention the collaboration with the BioSP unit of INRA on the modelling and mathematical analysis of spatial processes in ecology. In particular, several theses on this theme have been (or are being) co-supervised (J. Brasseur, J. Garnier, M.-E. Gil) (INRA co-directors: J. Coville and L. Roques).

Collaborations exist with the national industrial network: the collaboration between T. The collaboration between T. Gallouët and J.-M. Hérard, from EDF, is maintained by the co-supervision of CIFRE theses, which have led to numerous advances concerning the numerical simulation of multiphase flows. A contract also exists with Total (Pau), whose I2M members are : A. Benabdallah, F. Boyer, M. Cristofol, Y. Dermenjian, F Hubert and O. Poisson.

**Interaction with the socio-cultural environment**

As part of the dissemination of scientific culture,

– F. Hubert was invited to give a lecture to the general public as part of the Treize minutes de Marseille.

Marseille entitled “Forgotten medicines: consult your mathematician? She also gave lectures at the Forum Math, in Bastia, Aix-en-Provence, Marseille in 2012, 2013 and 2014, and an intervention in front of about 100 high school students in Besano ̧n 2013.

– G. Chapuisat gave a presentation in 2013 as part of the “Jeudis du CNRS”.

– M. Bostan gave a presentation: On the mathematical modelling of fusion by magnetic confinement in the framework of the Day: Sustainable development and energy transition in Saint Jérôme, on 24 May 2016 in front of 50 students.

– Since 2013, G. Chapuisat has participated every year in Math-en-Jeans with the Lycée International de Manosque. In 2012-2013, the students won the 1st prize at the national final of the C.Génial 2013 competition and they got the 2nd prize at the international CASTIC 2013 competition, Beijing. Their topic was “Will you catch the flu this winter?”.

– F. Hubert gave a presentation in 2012, in front of about 100 high school students in Besançon.

– F. Hubert, G. Chapuisat regularly give presentations in high schools.

– M. Cristofol has given lectures as part of the CPPM lecture series, Marseille and the IRIS association, La Ciotat in 2013.

**Involvement in training and research**

**Doctoral and post-doctoral supervision**

Theses defended between 2011 and 2016:

– T. Auphan, Analysis of models for ITER; Treatment of boundary conditions of systems modelling the on-board plasma in a tokamak, defended in 2014, supervisors: Ph. Angot and O. Guès, currently post-doctoral fellow IRSN, Cadarache ;

– H. Belghazi, Around some control problems of parabolic systems posed in a singular domain: Carleman’s inequalities and spectral inequality, defense in 2014, supervisors: A. Benabdallah and D. Téniou, currently assistant professor at Houari Boumédiène University (Alger);

– B. B. Bensiali, Numerical approximation for edge turbulence modelling, defended in 2014, supervisors: J. Liandrat and G. Chiavassa;

– S. Benzekry, Modelling, mathematical analysis and numerical analysis of anti-cancer therapies, defended in 2011, supervisors: D. Barbolosi, A. Benabdallah and F. Hubert, since September 2013 he is a CR at INRIA in Bordeaux;

– L. Buslig, Adaptive reconstruction by kriging: application in risk analysis, defended in 2014, supervisor: J. Liandrat ;

– C. Caldini-Queiros, Mathematical and numerical analysis of gyro-kinetic models, PhD thesis in 2013, supervisor: M. Bostan, currently post-doctoral fellow at Max-Planck Institut for Plasma Physics, Garchin;

– H. Charef, Macroscopic models of conduction and linearized elasticity for strongly heterogeneous and anisotropic media, PhD thesis in 2012, supervisor: A. Sili;

– F. Dardalhon, Numerical schemes for large scale simulation, PhD thesis in 2012, supervisor: F. Boyer, currently a secondary school teacher.

– W. Ding, Propagation phenomena of integro-difference equations and bistable reaction-diffusion equations in periodic habitats, defence in 2014, supervisors: F. Hamel and X. Liang, co-supervision with University of Science and Technology of China, currently post-doctoral fellow at University of New England, Australia;

– K. Dorogan, Numerical schemes for hybrid modelling of turbulent gas-particle flows, PhD thesis in 2011, CIFRE grant, supervisor: J.-M. Hérard, research engineer in the MRI department of EDF R and D since 2012;

– A. Fettah, Analysis of models in compressible fluid mechanics, defended in 2012, supervisor: T. Gallouët, currently MCF at the University of Tlemcen, Algeria;

– D. Fournier, Analysis and development of refinement methods for the transport equation, PhD thesis in 2011, supervisor: R. Herbin;

– J. Garnier, Mathematical analysis of population dynamics models: parabolic partial differential equations and integro-differential equations, defended in 2012, supervisors: F. Hamel and L. Roques, 2012 thesis prize from the University of Aix-Marseille, currently CR at the CNRS at the University of Savoie ;

– T.Giletti, Propagation phenomena inexcitable diffusive media: expansion velocities and lossy systems, defended in 2011, supervisor: F. Hamel; T. Giletti is a lecturer at the University of Lorraine;

– N.Hartung, Modelling of metastatic processes and in vitro imaging, defended in 2014, supervisors: G. Chapuisat and F. Hubert, currently a post-doctoral fellow at the department of clinical Pharmacy and Biochemistry, Universität Berlin, Germany;

– I. Kaddouri, Inverse problems for parabolic evolution problems with periodic coefficients, defense in 2014, supervisors: M. Cristofol and D. Téniou (cotutelle), currently in Master Actuarial Science at the University of Montreal;

– W.Kheriji, Pressure correction methods for compressible Navier-Stokes equations, PhD thesis in 2011, supervisor: R. Herbin ;

– Y. Liu, Contribution à la vérification et à la validation d’un modèle diphasique bifluide instation- naire, defended in 2013, CIFRE scholarship, supervisor: J.-M Hérard, currently at Linyi University (China);

– T-T. Nguyen, Explicit numerical schemes with staggered meshes for computation of compressible discharges, PhD thesis in 2013, supervisor: R. Herbin ;

– G. Olive, Controllability of coupled linear parabolic systems, defended in 2013, supervisors: A. Benabdallah and F. Boyer, currently post-doctoral fellow under the supervision of M. Tucsnak from Bordeaux University;

– H.Ouzzane, Carleman inequalities; applications to inverse problems and control some evolution problems, defended in 2014, supervisors: P. Gaitan and O. Zair (co-supervision), current-

MCF at the University Houari Boumédiène, Algiers, Algeria;

– K. Mallem, Convergence of the MAC scheme for incompressible Navier Stokes equations, defence in 2015, supervisor: R. Herbin, currently lecturer at the University of Skikda, Algeria ;

– X. Martin, Modelling fluid flows in an obstacle-encumbered environment, defended in 2015, CIFRE grant, director: J.-M Hérard, since 1 July, he is on fixed-term contract at IFPEN;

– F. Nabet, Finite volume schemes for multiphase problems, PhD thesis in 2014, supervisors: P. Bousquet and F. Boyer, currently post-doctoral fellow at Inria Lille and has just been awarded an MCF position at École Polytechnique.

– S. Pegaz-Fiornet, Study of models for hydrocarbon migration in basin simulators, defence in 2011, supervisor: T. Gallouët, thesis completed while already an IFP engineer;

– X. Si, On a Kriging/Subdivision Schemes coupling for the modelling of locally non-regular data, PhD thesis, supervisor: T. Gallët. X. Si, Sur un couplage Krigeage/Schémas de subdivision pour la modélisation de données localement non régulières, defended in 2013, supervisor: J. Liandrat,

– N. Therme, Numerical schemes for explosion simulation, defended in 2015, directors: R. Herbin, L. Gastaldo (IRSN, LIE, Cadarache), currently ATER at AMU ;

– X. Tunc, Modeling conductive faults for flow in porous media, submitted in 2012, CIF grant

nance in 2012, CIFRE grant, director: T. Gallouët, currently IFP engineer;

– M. Turkawi, Sobolev and Hardy-Sobolev spaces and divergence operator on graphs, defense in 2012, director: E. Russ ;

– P. Yin, Fictitious domain methods and adaptive simulation of Stefan problems, defence in 2011, supervisor: J. Liandrat, currently MCF at Jiangnan University (Wuxi, China);

– C. Zaza, Contribution to the numerical resolution of flows at any Mach number and fluid-porous coupling for the simulation of homogenised two-phase flows in nuclear components, defended in 2015, supervisors: R. Herbin, Ph. Angot, and M. Belliard (CEA Cadarache), currently post-doctoral fellow LIE (IRSN/DPAM).

Habilitations defended

– P. Bousquet, Density problems in Sobolev spaces with variety values. Regularity in calculus of variations. Critical cases for the raising of divergence, defended in 2013,

– M. Cristofol, Spectral analysis of waveguides in elasticity. Inverse problems for Schrödinger or parabolic operators, defence in 2011,

– M. Hauray, Mean-field limit and chaos propagation for particle systems, Gyro-kinetic and quasi-neutral limits for plasmas, defence in 2014,

– O. Poisson, Resonances for Multi-layered Acoustic Waveguides, defence in 2014.

Post-doctoral students

– Nina Aguillon, funded by Labex Archimede and supervised by F. Boyer (1 year in 2014-2015),

– Caroline Bauzet, funded by Labex Archimede and supervised by T. Gallouët and J. Charrier (1 year in 2013-2014),

– Aurélien Klak, funded by the ANRGYPSI, supervised by M.Hauray and A.Nouri (2 years in 2011-2013),

– Jonathan Martin, funded by ANR NONLOCAL and supervised by F. Hamel (1 year in 2015)

– Diana White, funded by the AMIDEX pharmato-ubules project and then the Plan cancer pharmato-tubules project, supervised by F. Hubert (1.5 years in 2015-2016),

The number of post-doctoral fellows is low because we lacked financial support.

**Doctoral training**

The team is very involved in the organisation and animation of doctoral training in Marseille. In particular, T. Gallouët is deputy director of the doctoral school ED 184 since 2013 and M. Bostan is member of the commission of this school. Moreover, Ph. Angot, F. Hamel, J. Liandrat, F. Boyer and M. Bostan have been in charge of the Master 2 “EDP et Calcul scientifique” mention Mathematics and Applications and A. Benabdallah was co-leader of the Master 1 of Mathematics from 2009 to 2012. In addition, there are many Master 2 internships supervised by members of the team.

Members of the team give courses in doctoral courses outside AMU:

– A. Benabdallah: Control of parabolic systems, Université Houari Boumédiène, Algiers, 2014,

– P. Bousquet: Mini-course at the Université Catholique de Louvain-la-Neuve, 2013,

– F. Hamel: Reaction-diffusion equations and front propagation, University of California, Berkeley (February 2013).

– S. Monniaux: PDEs in non-smooth domains, Darmstadt (Germany), 2011-2012.

**Pedagogical animation**

– R. Herbin was co-responsible for the mathematics degree for the period 2012-2015,

– M. Henry has been co-responsible for the mathematics licence since 2015,

– F. Boyer was co-leader of the master’s degree from 2012 to 2015, leader of the M2 EDP from 2012 to 2014 and leader of the preparation to the agrégation from 2014 to 2015,

– A. Benabdallah, G. Chapuisat, E. Ernst, M. Henry, R. Herbin and F. Hubert regularly participate in Studyrama, Paces et Etudiant,

– G. Chapuisat, F. Hubert and S. Monniaux are or have been members of the jury of the external agrégation (2014-…),

– M. Cristofol is responsible for mathematics teaching in the GEII department of the IUT,

– A. Benabdallah and F. Hubert are in charge of the maths-bio course of the mathematics licence,

– G. Chapuisat is responsible for the MPCI licence.