Stability of steady-state for 3-D hydrodynamic model of unipolar semiconductor with Ohmic contact boundary in hollow ball

doi:10.1016/j.jde.2020.12.027

CSpace

	Stability of steady-state for 3-D hydrodynamic model of unipolar semiconductor with Ohmic contact boundary in hollow ball
	Mei, Ming 1,2; Wu, Xiaochun 3; Zhang, Yongqian 4
	2021-03-15
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	277 页码:57-113
摘要	The existence of stationary subsonic solutions and their stability for 3-D hydrodynamic model of unipolar semiconductors with the Ohmic contact boundary have been open for long time due to some technical reason, as we know. In this paper, we consider 3-D radial solutions to the system in a hollow ball, and prove that the 3-D radial subsonic stationary solutions uniquely exist and are asymptotically stable, when the initial perturbations around the subsonic steady-state are small enough. Different from the existing studies on the radial solutions for fluid dynamics where the inner boundary of the hollow ball must be far away from the singular origin, here we may allow the chosen inner boundary arbitrarily close to the singular origin and reveal the relationship between the inner boundary and the large time behavior of the radial solution. This partially answers the open question of the stability of stationary waves subjected to the Ohmic contact boundary conditions in the multiple dimensional space. We also prove the existence of non-flat stationary subsonic solution, which essentially improve and develop the previous studies in this subject. The proof is based on the technical energy estimates in certain weighted Sobolev spaces, where the weight functions are artfully selected to be the distance of the targeted spatial location and the singular point. (C) 2020 Elsevier Inc. All rights reserved.
关键词	3-Dimensional hydrodynamic model Euler-Poisson equations Subsonic steady-state Asymptotic stability Radial solutions Weighted Sobolev spaces
DOI	10.1016/j.jde.2020.12.027
收录类别	SCI
语种	英语
资助项目	Joint Training Ph.D. Program of China Scholarship Council[201706100098] ; NSERC[RGPIN 354724-2016] ; FRQNT[256440] ; NSFC[11421061] ; Natural Science Foundation of Shanghai[15ZR1403900]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000610027200003
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/58080
专题	中国科学院数学与系统科学研究院
通讯作者	Wu, Xiaochun
作者单位	1.McGill Univ, Dept Math & Stat, Montreal, PQ H3A 2K6, Canada 2.Champlain Coll St Lambert, Dept Math, St Lambert, PQ J4P 3P2, Canada 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
推荐引用方式 GB/T 7714	Mei, Ming,Wu, Xiaochun,Zhang, Yongqian. Stability of steady-state for 3-D hydrodynamic model of unipolar semiconductor with Ohmic contact boundary in hollow ball[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2021,277:57-113.
APA	Mei, Ming,Wu, Xiaochun,&Zhang, Yongqian.(2021).Stability of steady-state for 3-D hydrodynamic model of unipolar semiconductor with Ohmic contact boundary in hollow ball.JOURNAL OF DIFFERENTIAL EQUATIONS,277,57-113.
MLA	Mei, Ming,et al."Stability of steady-state for 3-D hydrodynamic model of unipolar semiconductor with Ohmic contact boundary in hollow ball".JOURNAL OF DIFFERENTIAL EQUATIONS 277(2021):57-113.