Interfaces for 1-D degenerate keller-segel systems

Let us consider the Keller-Segel system of degenerate type (KS) _m with m >1 below. We prove the property of finite speed of propagation for weak solutions u with a certain regularity. Moreover, we investigate the interface curve which separates the regions (x, t) \in R× (0, T); u(x, t) > 0 and (x, t) R× (0, T); u(x, t) = 0. Concretely, we characterize the interface curve as the solution of a certain ordinary differential equation associated with (KS) _m .