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.

Degenerate parabolic equations (msc 35K65), Generalized solutions (msc 35Dxx), Dependence of solutions on initial and boundary data, parameters (msc 35B30), Motion of charged particles (msc 78A35)
Modelling, Analysis and Simulation [MAS]

Díaz, J.I, Galiano, G, & Jüngel, A. (1997). On a quasilinear degenerated system arising in semiconductors theory. Modelling, Analysis and Simulation [MAS]. CWI.