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SUMMARY:Nonlocal interaction PDEs with nonlinear diffusion - Marco Di Fran
 cesco (University of Bath)
DTSTART:20121018T140000Z
DTEND:20121018T150000Z
UID:TALK39425@talks.cam.ac.uk
CONTACT:Carola-Bibiane Schoenlieb
DESCRIPTION:The dynamics of interacting agents subject to binary forces ca
 n be often described at the microscopic level by a system of ODEs (with po
 ssible stochasticity) with discrete convolutions\, with a macroscopic coun
 terpart given by a so called nonlocal interaction pde. Both the microscopi
 c and the macroscopic models can be endowed with a gradient flow structure
  in a measure space which allows to give a mathematical statement of "conc
 entration" phenomena in finite time. This is done in particular for models
  with nonlocal attractive force without diffusion (no stochasticity). Mode
 ls with moderate repulsions and long range attraction give rise to continu
 um counterpart with a quadratic "porous medium" type term in the continuum
  pde\, which generates a threshold phenomena in the large time behaviour. 
 The main results described are the outcome of collaborations with J. A. Ca
 rrillo (Imperial College)\, M. Burger (Muenster) and other collaborators. 
 I will also briefly discuss the interplay with entropy solution theory (co
 llaboration with D. Matthes\, TU Munich\, plus some work in preparation).
LOCATION:MR 14\, CMS
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