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.
"Self-similar blow up with a continuous range of values of the aggregated mass for a degenerate Keller-Segel system." Adv. Differential Equations 16 (1/2) 85 - 112, January/February 2011.