Finite speed of propagation in 1-D degenerate Keller-Segel system (Q2883889)

This paper deals with a degenerate Keller-Segel type chemotaxis model with linear chemotactic sensitivity and porous medium type diffusion. A local-in-time weak solution with certain Lipschitz continuity is constructed through regularization and a priori estimates under suitable assumptions on initial data. As a consequence, the finite speed of propagation of the support of the solution is deduced and a region, in which the corresponding free boundary lies, is described.