Boundary layer analysis in the semiclassical limit of a quantum drift diffusion model

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:253

Article

Bian, Shen²  Chen, Li²  Dreher, Michael¹ 

[1] Univ Konstanz, Fachbereich Math & Stat, D-78457 Constance, Germany

[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

关键词: Quantum drift-diffusion model;    Boundary layer;    Elliptic system;    Variational methods;   

DOI  :  10.1016/j.jde.2012.03.008

来源: Elsevier

【 摘 要 】

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 confirm by means of numerical simulations that these remainder estimates are sharp. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free