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UID:4970@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20231121T093000
DTEND;TZID=Europe/Paris:20231121T170000
DTSTAMP:20240524T072506Z
URL:https://www.i2m.univ-amu.fr/evenements/journee-thematique-hyperbo-2023
 /
SUMMARY: (...): Journée thématique HYPERBO 2023
DESCRIPTION:: EDP hyperboliques\, conditions limites et méthodes numériqu
 es\nHyperbolic PDEs\, boundary conditions and numerical methods\n\nProgram
 me\n\n9h : Accueil Café\n10h - 11h15 : Bertrand Maury (Univ Paris Sud\, E
 NS)\n11h15 - 12h15 : Paola Goatin (INRIA Sophia Antipolis)\n12h15 - 14h : 
 Déjeuner (s'inscrire auprès des organisatrices)\n14h - 15h15 : Carlotta 
 Donadello (Univ Besançon)\n15h15 - 16h30 : Charlotte Perrin (CNRS\, Marse
 ille)\n16h30 : Clôture\, discussions\n\nAbstracts\n\n\n\n\nCarlotta Donad
 ello :  Conservation laws on a star-shaped network\n\nHyperbolic conserva
 tion laws defined on oriented graphs are widely used in the modeling of a 
 variety of phenomena such as vehicular and pedestrian traffic\, irrigation
  channels\, blood circulation\, gas pipelines\, structured population dyna
 mics. From the point of view of the mathematical analysis each of these si
 tuations demands for a different definition of admissible solution\, encod
 ing in particular the node coupling between incoming and outgoing edges wh
 ich is the most coherent with physical observations.\n\n\nA comprehensive 
 study of the necessary and sufficient properties of the coupling condition
 s which lead to well-posedness of the corresponding admissible solutions i
 s available in the framework of conservation laws with discontinuous flux\
 , which can be seen as a simple $1-1$ network. A similar theory for conser
 vation laws on star-shaped graph is at its beginning. In particular\, the 
 characterization of family of solutions obtained as limits of regularizing
  approximations\, such as vanishing viscosity limits\, is still a partiall
 y open problem. In this talk we’ll provide a general introduction to the
  topic\, an overview of the most recent results and some explicit examples
 .\n\n\n\n\n\nPaola Goatin : Nonlocal macroscopic models of multi-populatio
 n pedestrian flows for walking facilities optimization\n\n\nWe propose a n
 onlocal macroscopic pedestrian flow model for several populations with dif
 ferent destinations trying to avoid each other in a confined environment\,
  where the nonlocal term accounts for anisotropic interactions\, mimicking
  the effect of different cones of view\, and the presence of walls or othe
 r obstacles in the domain. In particular\, obstacles can be incorporated i
 n the density variable\, thus avoiding to include them in the vector field
  of preferred directions.\n\nThe well posedness of the model is studied an
 alytically and numerical tests confirm that each population manages to ev
 ade both the presence of the obstacles and the other populations.\n\n\nFin
 ally\, we study the optimization of evacuation times. In particular\, the 
 optimal position of the obstacles is obtained using a total travel time mi
 nimisation processes.\n\n\n\n\n\n\n\nBertrand Maury : Mouvements de foules
  sociales : à la frontière du monde hilbertien\n\nUn grand nombre de ph
 énomènes physiques recèle une structure de flot de gradient\, ou de de 
 système hamiltonien (que l’on peut voir comme une version inertielle du
  flot de gradient).\nCela signifie qu’il existe une fonction sous-jacent
 e des variables d’état (de positions s’il s’agit par exemple de par
 ticules)\, de type énergie potentielle dans un contexte mécanique\, qui 
 conditionne l’évolution du système. Dans la version non inertielle\, l
 ’état du système « glisse » suivant la ligne de plus grande pente de
  cette fonction\, qui conditionne donc entièrement le comportement global
  du système. Lorsqu’il s’agit de particules\, avec une fonctionnelle 
 qui ne dépend que de leurs positions relatives\, cette structure variatio
 nnelle implique un principe d’action réaction.\nNous proposons d’expl
 orer le rôle joué par cette structure dans les modèles de mouvements de
  foules. Nous nous intéresserons en particulier aux limites possibles des
  modèles de type flot de gradient lorsque la métrique dégénère\, cond
 uisant à une violation du principe d’action-réaction qui est réaliste
  pour des entités dotées de capacités cognitives et décisionnelles.\n\
 n\n\n\n\n\n\nCharlotte Perrin : Hard congestion limit of the p-system in t
 he BV setting\n\nIn this talk\, I will discuss the transition from a compr
 essible (inviscid) system with singular pressure towards a mixed compressi
 ble-incompressible system modeling partially congested dynamics. The two s
 ystems may be used for the modeling of mixtures\, of collective motions\, 
 or partially free surface flows. From the mathematical point of view\, I w
 ill present a first convergence result for small BV perturbations of a ref
 erence state represented by one or more partially congested propagating fr
 onts.\n\n\n\n\n\n\n\n\nOrganisation : Raphaèle Herbin\, Charlotte Perrin
CATEGORIES:Groupe de travail,HYPERBO,Journée(s),Manifestation
 scientifique
LOCATION:St Charles - FRUMAM\, 3\, place Victor Hugo\, Marseille\, 13003\, 
 France
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 seille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=St Charles - FRUMAM:geo
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TZID:Europe/Paris
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DTSTART:20231029T020000
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