The combined viscous semi-classical limit for a quantum hydrodynamic system with barrier potential

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:425

Article

Dreher, Michael¹  Schnur, Johannes² 

[1] Heriot Watt Univ, Sch Math & Comp Sci, Edinburgh EH14 4AS, Midlothian, Scotland

[2] Univ Konstanz, Dept Math & Stat, D-78457 Constance, Germany

关键词: Boundary layers;    Quantum hydrodynamics;    Remainder estimates;   

DOI  :  10.1016/j.jmaa.2015.01.019

来源: Elsevier

【 摘 要 】

We investigate the viscous model of quantum hydrodynamics, which describes the charge transport in a certain semiconductor. Quantum mechanical effects lead to third order derivatives, turning the stationary system into an elliptic system of mixed order in the sense of Douglis-Nirenberg. In the case most relevant to applications, the semiconductor device features a piecewise constant barrier potential. In the case of thermodynamic equilibrium, we obtain asymptotic expansions of interfacial layers of the particle density in neighbourhoods of the jump points of this barrier potential, and we present rigorous proofs of uniform estimates of the remainder terms in these asymptotic expansions. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free