Quasilinear Degenerated System Arising in Semiconductors Theory. Part 1.211 Existence and Uniqueness of Solutions. Modelling, Analysis and Simulation

摘要

A drift-diffusion model for semiconductors with nonlinear diffusion is211u001econsidered. The model consists of two quasilinear degenerated parabolic equations 211u001efor the carrier densities and the Poisson equation for the electric potential. 211u001eThe authors also assume Lipshitz continuous non linearities in the drift and 211u001egeneration-recombination terms. Existence of weak solutions is proven by using a 211u001eregularization technique. Uninqueness of solutions is proven when either the 211u001ediffusion term gamma is strictly increasing and solutions have spatial 211u001ederivatives in L(sup 1)(Qr) or when gamma is decreasing and a suitable entropy 211u001econditions is fulfilled by the electric is fulfilled by the electric potential.