On a quasilinear degenerated system arising in semiconductors theory

A drift-diffusion model for semiconductors with nonlinear diffusion is considered. The model consists of two quasilinear degenerated parabolic equations for the carrier densities and the Poisson equation for the electric potential. We also assume Lipschitz continuous non linearities in the drift and {em generation-recombination terms. Existence of weak solutions is proven by using a regularization technique. Uniqueness of solutions is proven when either the diffusion term $varphi$ is strictly increasing and solutions have spatial derivatives in $L^1(Q_T)$ or when $varphi$ is non decreasing and a suitable entropy condition is fullfilled by the electric potential.