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Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices
Huang, Feimin1,2; Li, Tianhong3; Yu, Huimin4; Yuan, Difan1,2
2018-06-01
发表期刊ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
ISSN0044-2275
卷号69期号:3页码:12
摘要We are concerned with the global existence and large time behavior of entropy solutions to the one-dimensional unipolar hydrodynamic model for semiconductors in the form of Euler-Poisson equations in a bounded interval. In this paper, we first prove the global existence of entropy solution by vanishing viscosity and compensated compactness framework. In particular, the solutions are uniformly bounded with respect to space and time variables by introducing modified Riemann invariants and the theory of invariant region. Based on the uniform estimates of density, we further show that the entropy solution converges to the corresponding unique stationary solution exponentially in time. No any smallness condition is assumed on the initial data and doping profile. Moreover, the novelty in this paper is about the unform bound with respect to time for the weak solutions of the isentropic Euler-Poisson system.
关键词Isentropic Euler-Poisson equations Compensated compactness Entropy solution Vanishing viscosity Large time behavior
DOI10.1007/s00033-018-0968-z
语种英语
资助项目National Center for Mathematics and Interdisciplinary Sciences, AMSS, CAS ; NSFC[11371349] ; NSFC[11688101] ; NSFC[11671237] ; Natural Science Foundation of Shandong Province[ZR2015AM001] ; China Scholarship Council[201704910503]
WOS研究方向Mathematics
WOS类目Mathematics, Applied
WOS记录号WOS:000433069100001
出版者SPRINGER BASEL AG
引用统计
文献类型期刊论文
条目标识符http://ir.amss.ac.cn/handle/2S8OKBNM/30337
专题应用数学研究所
通讯作者Huang, Feimin
作者单位1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Chinese Acad Sci, AMSS, Hua Loo Keng Key Lab Math, Beijing 100190, Peoples R China
4.Shandong Normal Univ, Dept Math, Jinan 250014, Shandong, Peoples R China
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Huang, Feimin,Li, Tianhong,Yu, Huimin,et al. Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices[J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK,2018,69(3):12.
APA Huang, Feimin,Li, Tianhong,Yu, Huimin,&Yuan, Difan.(2018).Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices.ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK,69(3),12.
MLA Huang, Feimin,et al."Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices".ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 69.3(2018):12.
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