Boundary layer analysis in the semiclassical limit
of a quantum drift diffusion model
Sh. Bian and L. Chen and M. Dreher
Abstract.
We study a singularly perturbed elliptic second order system in one space
variable as it appears in a stationary quantum drift diffusion model of a
semiconductor. We prove the existence of solutions and their uniqueness as
minimizers of a certain functional and determine rigorously the principal
part of an asymptotic expansion of a boundary layer of those solutions. We
prove analytical estimates of the remainder terms of this asymptotic
expansion, and numerical simulations hint that these
remainder estimates are sharp.
J. Differential Equations
253 (2012), 356-377.
The paper is available
here.
