The quasineutral limit problem in semiconductor sciences (Q2504954)

This paper is a review of several works by the author on various mathematical models used for description of the electrical current transport in semiconductors. The models can be broadly subdivided in two classes: kinetic and fluid dynamics type. Each of these, in addition, can be treated either semiclassically or quantum mechanically. All works by the author reviewed in this paper are of classical hydrodynamics type involving nonlinear PDEs. In some limits discussed in the paper the results are also applicable to plasma dynamics. The mathematical proofs are based on entropy methods and weak compactness arguments. First, by constructing the entropy functional uniform a priori estimates are obtained. Then, weak compactness methods are applied to check the convergence of the obtained results.