Finite mass self-similar blowing-up solutions of a chemotaxis system with non-linear diffusion

Abstract

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 $d?3$.

References in corpus (2)

• Critical dynamics of self-gravitating Langevin particles and bacterial populations
• Critical chemotactic collapse

Cited by in corpus (2)

• Critical mass on the Keller-Segel system with signal-dependent motility
• A semilinear parabolic-elliptic chemotaxis system with critical mass in any space dimension