Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices

doi:10.1007/s00033-018-0968-z

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 应用数学研究所

	Large time behavior of entropy solutions to one-dimensional unipolar hydrodynamic model for semiconductor devices
	Huang, Feimin1,2 ; Li, Tianhong 3; Yu, Huimin 4; Yuan, Difan 1,2
刊名	ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
	2018-06-01
卷号	69 期号:3 页码:12
关键词	Isentropic Euler-Poisson equations Compensated compactness Entropy solution Vanishing viscosity Large time behavior
ISSN号	0044-2275
DOI	10.1007/s00033-018-0968-z
英文摘要	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.
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
语种	英语
出版者	SPRINGER BASEL AG
WOS记录号	WOS:000433069100001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/30336]
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
推荐引用方式 GB/T 7714	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.