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SUMMARY:Asymptotic behaviour of diffusing and self-attracting particles - 
 Franca Hoffmann (University of Cambridge)
DTSTART:20151111T160000Z
DTEND:20151111T170000Z
UID:TALK62365@talks.cam.ac.uk
CONTACT:Adam Kashlak
DESCRIPTION:We study interacting particles behaving according to a\nreacti
 on-diffusion equation with non-linear diffusion and non-local attractive i
 nteraction. This class of equations has a very nice gradient flow structur
 e that allows us to make links to variations of well-known functional ineq
 ualities (Hardy-Littlewood-Sobolev inequality\, logarithmic Sobolev inequa
 lity). Depending on the non-linearity of the diffusion\, the choice of int
 eraction potential and the dimensionality\, we obtain different regimes. O
 ur goal is to understand better the asymptotic behaviour of solutions in e
 ach of these regimes\, starting with the fair-competition regime where att
 ractive and repulsive forces are in balance. This is joint work with José
  A. Carrillo and Vincent Calvez.
LOCATION:MR14\, Centre for Mathematical Sciences
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