A NONLINEAR DRIFT-DIFFUSION SYSTEM WITH ELECTRIC CONVECTION ARISING IN ELECTROPHORETIC AND SEMICONDUCTOR MODELING

A multi-dimensional transient drift-diffusion model for (at most) thre e charged particles, consisting of the continuity equations for the co ncentrations of the species and the Poisson equation for the electric potential, is considered. The diffusion terms depend on the concentrat ions. Such a system arises in electrophoretic modeling of three specie s (neutrally, positively and negatively charged) and in semiconductor theory for two species (positively charged holes and negatively charge d electrons). Diffusion terms of degenerate type are also possible in semiconductor modeling. For the initial boundary value problem with mi xed Dirichlet-Neumann boundary conditions and general reaction rates, a global existence result is proved. Uniqueness of solutions follows i n the Dirichlet boundary case if the diffusion terms are uniformly par abolic or if the initial and boundary densities are strictly positive. Finally, we prove that solutions exist which are positive uniformly i n time and globally bounded if the reaction rates satisfy appropriate growth conditions.