3 November 2008

17:00

Philippe Laurençot

Abstract

In space dimension 2, it is well-known that the Smoluchowski-Poisson
system (also called the simplified or parabolic-elliptic Keller-Segel
chemotaxis model) exhibits the following phenomenon: there is a critical
mass above which all solutions blow up in finite time while all solutions
are global below that critical mass. We will investigate the case of the
critical mass along with the stability of self-similar solutions with
lower masses. We next consider a generalization to several space
dimensions which involves a nonlinear diffusion and show that a similar
phenomenon takes place but with some different features.