Space localization and uniqueness of solutions of a quasilinear parabolic system arising in semiconductor theory

Abstract

A degenerate parabolic system consisting in two continuity equations for densities of charged particles and in the Poisson equation for an electric potential is considered. We show the finite speed of propagation, a waiting time property for the vacuum (null) sets and a property of formation of vacuum. The proofs are based on energy methods. Furthermore, some results on the uniqueness of solutions are proved by using different duality methods.