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TZID:Europe/Paris
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UID:5104@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20240402T100000
DTEND;TZID=Europe/Paris:20240402T110000
DTSTAMP:20240524T072506Z
URL:https://www.i2m.univ-amu.fr/evenements/nonlocal-aggregation-diffusion-
 equations-fast-diffusion-and-partial-concentration/
SUMMARY: (...): Nonlocal Aggregation-Diffusion Equations: fast diffusion an
 d partial concentration
DESCRIPTION:: We will discuss several recent results for aggregation-diffus
 ion equations related to partial concentration of the density of particles
 . Nonlinear diffusions with homogeneous kernels will be reviewed quickly i
 n the case of degenerate diffusions to have a full picture of the problem.
  Most of the talk will be devoted to discuss the less explored case of fas
 t diffusion with homogeneous kernels with positive powers. We will first c
 oncentrate in the case of stationary solutions by looking at minimisers of
  the associated free energy showing that the minimiser must consist of a r
 egular smooth solution with singularity at the origin plus possibly a part
 ial concentration of the mass at the origin. We will give necessary condit
 ions for this partial mass concentration to and not to happen. We will the
 n look at the related evolution problem and show that for a given confinem
 ent potential this concentration happens in infinite time under certain co
 nditions. We will briefly discuss the latest developments when we introduc
 e the aggregation term. This talk is based on a series of works in collabo
 ration with M. Delgadino\, J. Dolbeault\, A. Fernández\, R. Frank\, D. G
 ómez-Castro\, F. Hoffmann\, M. Lewin\, and J. L\, Vázquez.
CATEGORIES:Séminaire,Analyse Appliquée
LOCATION:Saint-Charles - FRUMAM  (2ème étage)\, 3 Place Victor Hugo\, Mar
 seille\, 13003\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=3 Place Victor Hugo\, Marse
 ille\, 13003\, France;X-APPLE-RADIUS=100;X-TITLE=Saint-Charles - FRUMAM  (
 2ème étage):geo:0,0
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DTSTART:20240331T030000
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