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SUMMARY:Nonlocal Aggregation-Diffusion Equations: fast diffusion and parti
 al concentration - José Carrillo (University of Oxford)
DTSTART:20230227T140000Z
DTEND:20230227T150000Z
UID:TALK195163@talks.cam.ac.uk
CONTACT:Daniel Boutros
DESCRIPTION:We will discuss several recent results for aggregation-diffusi
 on equations related to partial concentration of the density of particles.
  Nonlinear diffusions with homogeneous kernels will be reviewed quickly in
  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 fast
  diffusion with homogeneous kernels with positive powers. We will first co
 ncentrate in the case of stationary solutions by looking at minimisers of 
 the associated free energy showing that the minimiser must consist of a re
 gular smooth solution with singularity at the origin plus possibly a parti
 al concentration of the mass at the origin. We will give necessary conditi
 ons for this partial mass concentration to and not to happen. We will then
  look at the related evolution problem and show that for a given confineme
 nt potential this concentration happens in infinite time under certain con
 ditions. We will briefly discuss the latest developments when we introduce
  the aggregation term. This talk is based on a series of works in collabor
 ation with M. Delgadino\, J. Dolbeault\, A. Fernández\, R. Frank\, D. Gó
 mez-Castro\, F. Hoffmann\, M. Lewin\, and J. L. Vázquez.
LOCATION:CMS\, MR13
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