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

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• 作者：Shen Bian^a ; ^{bs09@mails.tsinghua.edu.cn} ; Li Chen^a ; ^{lchen@math.tsinghua.edu.cn} ; Michael Dreher^b ; ^{michael.dreher@uni-konstanz.de}
• 关键词：35J50 ; 76N20 ; 81Q20
• 刊名：Journal of Differential Equations
• 出版年：2012
• 出版时间：1 July, 2012
• 年：2012
• 卷：253
• 期：1
• 页码：356-377
• 全文大小：274 K

文摘

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.