Philippe Laurençot
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Critical mass in a generalized Smoluchowski-Poisson system

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Philippe Laurençot

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Université Paul Sabatier, Toulouse
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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.