Optimal behavior of the support of the solutions to a class of degenerate parabolic systems

Abstract

In this paper we deal with a class of degenerate/singular quasilinear parabolic systems. We study a Cauchy problem in ${\mathbb{R}}^N$ with an initial datum in $L^1$. Sharp $L^{\infty }$ estimates are proved. In the degenerate case, assuming that the initial datum has compact support, we prove the optimal speed of propagation of the support.