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A Nonlinear Drift ‐ Diffusion System with Electric Convection Arising in Electrophoretic and Semiconductor Modeling
Author(s) -
Jüngel Ansgar
Publication year - 1997
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.3211850108
Subject(s) - uniqueness , boundary value problem , diffusion , poisson's equation , mathematical analysis , mathematics , semiconductor , degenerate energy levels , dirichlet boundary condition , boundary (topology) , dirichlet distribution , neumann boundary condition , physics , thermodynamics , quantum mechanics
A multi‐dimensional transient drift‐diffusion model for (at most) three charged particles, consisting of the continuity equations for the concentrations of the species and the Poisson equation for the electric potential, is considered. The diffusion terms depend on the concentrations. Such a system arises in electrophoretic modeling of three species (neutrally, positively and negatively charged) and in semiconductor theory for two species (positively charged holes and negatively charged electrons). Diffusion terms of degenerate type are also possible in semiconductor modeling. For the initial boundary value problem with mixed Dirichlet ‐ Neumann boundary conditions and general reaction rates, a global existence result is proved. Uniqueness of solutions follows in the Dirichlet boundary case if the diffusion terms are uniformly parabolic or if the initial and boundary densities are strictly positive. Finally, we prove that solutions exist which are positive uniformly in time and globally bounded if the reaction rates satisfy appropriate growth conditions.