Self-similar blow up with a continuous range of values of the aggregated mass for a degenerate Keller-Segel system

Abstract

In this paper we show that there exist radial solutions of the Keller-Segel system with porous medium like diffusion and critical exponents that blow up in a self-similar manner with a continuous range of masses. The situation is very different from the one that takes place for the usual Keller-Segel system with semilinear diffusion, that for critical nonlinearities yields blow up with a discrete set of values for the mass.