A nonlinear drift-diffusion system with electric convection arising in electrophoretic and semiconductor modeling. (English) Zbl 1157.35406
The author considers a multidimensional transient drift-diffusion model for at least three charged particles, consisting of the continuity equations for the concentrations of the species and for the Poisson equation for the electric potential. The diffusion term depends on the concentrations. Such a system arises in electrophoretic modeling of three species (neutrally, positively and negatively charged) as well as in semiconductor theory for two species (positively charged holes and negatively charged electrons).
For the initial value problems with mixed conditions of Dirichlet-Neumann type, and general reaction rates, a global existence result is proved. Uniqueness of solutions follows in the Dirichlet case if the diffusion terms are uniformly parabolic or if the initial data and boundary densities are strictly positive. Finally, it is proved that solutions exist which are positive uniformly in time and globally bounded if the reaction rates satisfy suitable growth conditions.
For the initial value problems with mixed conditions of Dirichlet-Neumann type, and general reaction rates, a global existence result is proved. Uniqueness of solutions follows in the Dirichlet case if the diffusion terms are uniformly parabolic or if the initial data and boundary densities are strictly positive. Finally, it is proved that solutions exist which are positive uniformly in time and globally bounded if the reaction rates satisfy suitable growth conditions.
Reviewer: Dian K. Palagachev (Bari) (MR1452478)
MSC:
| 35K57 | Reaction-diffusion equations |
| 78A35 | Motion of charged particles |
| 35K65 | Degenerate parabolic equations |
| 35D05 | Existence of generalized solutions of PDE (MSC2000) |
| 35B35 | Stability in context of PDEs |
| 92E20 | Classical flows, reactions, etc. in chemistry |
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