ON A QUASILINEAR DEGENERATE SYSTEM ARISING IN SEMICONDUCTORS THEORY. PART I: EXISTENCE AND UNIQUENESS OF SOLUTIONS∗

Abstract. A drift-diffusion model for semiconductors with nonlinear diffusion is considered. The model consists of two quasilinear degenerate parabolic equations for carrier densities and the Poisson equation for electric potential. We assume Lipschitz continuous nonlinearities in the drift and generation-recombination terms. Existence of weak solutions is proven by using a regularization technique. Uniqueness of solutions is proven when either the diffusion term ϕ is strictly increasing and solutions have spatial derivatives in L1(QT) or when ϕ is non-decreasing and a suitable entropy condition is fullfilled by the electric potential. Key words. Quasilinear degenerate system, semiconductors. AMS subject classifications. 35K65, 35D05, 35B30, 78A35