1 research outputs found
Finite mass self-similar blowing-up solutions of a chemotaxis system with non-linear diffusion
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 such that all the solutions with
initial data of mass smaller or equal to exist globally while the
solution blows up in finite time for a large class of initial data with mass
greater than . Unlike in space dimension 2, finite mass self-similar
blowing-up solutions are shown to exist in space dimension