双极非等熵Euler-Poisson方程非常数平衡解的稳定性

数学物理学报 ›› 2016, Vol. 36 ›› Issue (5): 978-996.

双极非等熵Euler-Poisson方程非常数平衡解的稳定性

李新, 王术, 冯跃红

北京工业大学应用数理学院北京 100124

收稿日期:2015-11-13 修回日期:2016-04-16 出版日期:2016-10-26 发布日期:2016-10-26
通讯作者: 冯跃红,E-mail:fyh@bjut.edu.cn E-mail:fyh@bjut.edu.cn
作者简介:李新,E-mail:lixin91600@163.com;王术,E-mail:@bjut.edu.cn;冯跃红,E-mail:fyh@bjut.edu.cn
基金资助:
国家自然科学基金（11371042）、北京市自然科学基金（1132006，1164010）、北京市教委重点资助项目、首都社会建设和社会管理协同创新中心资助项目、中国博士后科学基金资助项目、朝阳区博士后工作经费资助项目、北京工业大学基础研究基金项目、北京市博士后科研活动经费资助项目、北京市教育委员会科技计划一般项目和2016年度北京市留学人员科技活动择优资助项目资助

Stability of Non-Constant Equilibrium Solutions for Bipolar Non-Isentropic Euler-Poisson Equations

Li Xin, Wang Shu, Feng Yuehong

College of Applied Sciences, Beijing University of Technology, Beijing 100124

Received:2015-11-13 Revised:2016-04-16 Online:2016-10-26 Published:2016-10-26
Supported by:
Supported by the NSFC (11371042), the BNSF (1132006, 1164010), the Key Fund of the Beijing Education Committee, the Collaborative Innovation Center on Beijing Society-Building and Social Governance, the China Postdoctoral Science Foundation Funded Project, the Government of Chaoyang District Postdoctoral Research Foundation, the Beijing University of Technology Foundation Funded Project, Beijing Prosdoctoral Research Foundation, the General Project of Scientific Research Project of the Beijing Education Committee and the 2016 Beijing Project of Scientific Activities for the Excellent Students Studying Abroad

摘要/Abstract

摘要：

该文考察源自半导体材料科学中的双极非等熵Euler-Poisson方程组.运用对称子的技巧与时空混合导数迭代方法，研究了三维空间环上的周期问题.在初值为一个非常数平衡解的小摄动条件下，证明了当时间趋于无穷大时，该问题存在唯一整体光滑解，且按指数速率收敛至平衡态.这种粒子输运现象反映了双极非等熵与单极非等熵、双极等熵Euler-Poisson方程组之间存在本质区别.

关键词: 双极非等熵Euler-Poisson方程组, 半导体, 整体光滑解

Abstract:

This article is concerned with the bipolar non-isentropic Euler-Poisson equations in semiconductors. We investigated, by means of an induction argument on the order of the mixed time-space derivatives of solutions in energy estimates and the techniques of symmetrizer, the periodic problem in a three-dimensional torus. Under the assumption that initial data are close to a non constant equilibrium solutions, we prove that the smooth solutions of this problem converge to a steady state with exponential decay rates as the time goes to the infinity. This phenomenon on the charge transport shows the essential difference among the bipolar non-isentropic, the unipolar non-isentropic and the bipolar isentropic Euler-Poisson equations.

Key words: Bipolar non-isentropic Euler-Poisson equations, Semiconductors, Global Smooth Solutions

中图分类号:

O175

李新, 王术, 冯跃红. 双极非等熵Euler-Poisson方程非常数平衡解的稳定性[J]. 数学物理学报, 2016, 36(5): 978-996.

Li Xin, Wang Shu, Feng Yuehong. Stability of Non-Constant Equilibrium Solutions for Bipolar Non-Isentropic Euler-Poisson Equations[J]. Acta mathematica scientia,Series A, 2016, 36(5): 978-996.

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