文献类型：期刊文献

中文题名：有界域上一维双极量子力学模型解的经典极限（英文）

英文题名：The classical limit to a bipolar quantum hydrodynamic model of semiconductors in a bounded domain

作者：孔海阅[1];黎野平[2]

机构：[1]上海师范大学数理学院,上海200234;[2]华东理工大学理学院,上海200237

年份：2015

卷号：44

期号：2

起止页码：111

中文期刊名：上海师范大学学报（自然科学版）

外文期刊名：Journal of Shanghai Normal University(Natural Sciences)

收录：CSTPCD

基金：Supproted by the Natioinal Science Foundation of China(11171223);the Innovation Program of Shanghai Municipal Education Commission(13ZZ109)

语种：中文

中文关键词：双极;量子力学模型;经典极限

外文关键词：bipolar; quantum hydrodynamic model; classical limit

摘要：考虑一维双极等熵量子力学模型.首先,对方程进行一些变形,利用Poincarés不等式及函数收敛和弱收敛的一些性质,得到了稳态解的经典极限,即当普朗克常量ε趋于0时,量子力学模型方程的稳态解趋于经典力学模型方程的稳态解.然后,利用非稳态解已有的一些结论和Sobolev不等式,Schwartz不等式,Gronwall不等式及一些能量估计,得到了非稳态解的经典极限,即量子力学模型方程的光滑解趋于经典力学模型方程的光滑解.
We consider a one-dimensional bipolar isentropic quantum hydrodynamical model from semiconductor devices. First, we discuss the classical limit of the stationary solution. Then we discuss the classical limit of the non-stationary initial boundary problem for a one-dimensional case in a bounded domain. We show that the solutions to the quantum hydrodynamic model of semiconductors approaches that to the hydrodynamic model of semiconductors as the sealed Planck constants ε tends to zero.