  For a specific choice of the diffusion, the parabolic-elliptic
Patlak-Keller-Segel system with non-linear diffusion (also referred to as the
quasi-linear Smoluchowski-Poisson equation) exhibits an interesting threshold
phenomenon: there is a critical mass $M_c>0$ such that all the solutions with
initial data of mass smaller or equal to $M_c$ exist globally while the
solution blows up in finite time for a large class of initial data with mass
greater than $M_c$. Unlike in space dimension 2, finite mass self-similar
blowing-up solutions are shown to exist in space dimension $d?3$.
