Existence and stability of steady-state of one-dimensional quantum hydrodynamic system for semiconductors

doi:10.1016/j.jde.2006.02.002

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	Existence and stability of steady-state of one-dimensional quantum hydrodynamic system for semiconductors
	Huang, Feimin; Li, Hai-Liang ; Matsumura, Akitaka
	2006-06-01
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	225 期号:1 页码:1-25
摘要	A transient quantum hydrodynamic system for charge density, current density and electrostatic potential is considered in spatial one-dimensional real line. The equations take the form of classical Euler-Poisson system with additional dispersion caused by the quantum (Bohm) potential and used, for instance, to account for quantum mechanical effects in the modelling of charge transport in ultra submicron semiconductor devices such as resonant tunnelling trough oxides gate and inversion layer energy quantization and so on. The existence and uniqueness and long time stability of steady-state solution with spatial different end states and large strength is proven in Sobolev space. To guarantee the existence and stability, we propose a stability condition which can be viewed as a quantum correction to classical subsonic condition. Furthermore. since the argument for classical hydrodynamic equations does not apply here due to the dispersion term. we also show the local-in-time existence of strong solution in terms of a reformulated system for the charge density and the electric field consisting of two coupled semilinear (spatial) fourth-order wave type equations. (c) 2006 Elsevier Inc. All rights reserved.
关键词	quantum hydrodynamic models existence and exponential stability of steady-state global existence of smooth solutions semiconductor model
DOI	10.1016/j.jde.2006.02.002
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000238045600001
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/2801
专题	应用数学研究所
通讯作者	Huang, Feimin
作者单位	1.Acad Sinica, Inst Appl Math, AMSS, Beijing 100080, Peoples R China 2.Capital Normal Univ, Dept Math, Beijing 100037, Peoples R China 3.Osaka Univ, Dept Pure & Appl Math, Grad Sch Informat Sci & Technol, Toyonaka, Osaka 5600043, Japan
推荐引用方式 GB/T 7714	Huang, Feimin,Li, Hai-Liang,Matsumura, Akitaka. Existence and stability of steady-state of one-dimensional quantum hydrodynamic system for semiconductors[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2006,225(1):1-25.
APA	Huang, Feimin,Li, Hai-Liang,&Matsumura, Akitaka.(2006).Existence and stability of steady-state of one-dimensional quantum hydrodynamic system for semiconductors.JOURNAL OF DIFFERENTIAL EQUATIONS,225(1),1-25.
MLA	Huang, Feimin,et al."Existence and stability of steady-state of one-dimensional quantum hydrodynamic system for semiconductors".JOURNAL OF DIFFERENTIAL EQUATIONS 225.1(2006):1-25.