Drift-Diffusion Equations and Applications

Abstract

We shall discuss a variety of drift-diffusion equations and their properties. The choice is not intended to be comprehensive, rather it reflects to considerable extent the author’s interests, and the cited references mention numerous other related papers. We begin with a short description of results for the ”classical” drift-diffusion equations for semiconductors, then consider variations and, finally, an application. To minimize technical difficulties we shall always assume that all known functions are smooth in their variables otherwise specified, and all mathematically irrelevant constants will be set to unity. The interested reader will find more general situations discussed in the given references.

The solutions to be found are also to be understood in the usual weak sense. Nevertheless we shall almost always use classical notation to make the key steps evident. Again, a more precise formulation can be found in the references.