On exponential stability of a semilinear wave equation with variable coefficients under the nonlinear boundary feedback

doi:10.1016/j.na.2009.05.018

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	On exponential stability of a semilinear wave equation with variable coefficients under the nonlinear boundary feedback
	Guo, Bao-Zhu1,2 ; Shao, Zhi-Chao 2,3
刊名	NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
	2009-12-15
卷号	71 期号:12 页码:5961-5978
关键词	Semilinear wave equation Nonlinear boundary feedback Riemannian geometry method Variable coefficients
ISSN号	0362-546X
DOI	10.1016/j.na.2009.05.018
英文摘要	The uniform stabilization of an originally regarded nondissipative system described by a semilinear wave equation with variable coefficients under the nonlinear boundary feedback is considered. The existence of both weak and strong solutions to the system is proven by the Galerkin method. The exponential stability of the system is obtained by introducing an equivalent energy function and using the energy multiplier method on the Riemannian manifold. This equivalent energy function shows particularly that the system is essentially a dissipative system. This result not only generalizes the result from constant coefficients to variable coefficients for these kinds of semilinear wave equations but also simplifies significantly the proof for constant coefficients case considered in [A. Guesmia, A new approach of stabilization of nondissipative distributed systems, SIAM J. Control Optim. 42 (2003) 24-52] where the system is claimed to be nondissipative. (C) 2009 Elsevier Ltd. All rights reserved.
资助项目	National Natural Science Foundation of China ; National Research Foundation of South Africa ; Claude Leon Foundation in South Africa ; University of International Business and Economics[31042]
WOS研究方向	Mathematics
语种	英语
出版者	PERGAMON-ELSEVIER SCIENCE LTD
WOS记录号	WOS:000272606300006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/7766]
专题	系统科学研究所
通讯作者	Guo, Bao-Zhu
作者单位	1.Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Int Business & Econ, Sch Informat Technol, Beijing 100029, Peoples R China 3.Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Wits, Johannesburg, South Africa
推荐引用方式 GB/T 7714	Guo, Bao-Zhu,Shao, Zhi-Chao. On exponential stability of a semilinear wave equation with variable coefficients under the nonlinear boundary feedback[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,2009,71(12):5961-5978.
APA	Guo, Bao-Zhu,&Shao, Zhi-Chao.(2009).On exponential stability of a semilinear wave equation with variable coefficients under the nonlinear boundary feedback.NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS,71(12),5961-5978.
MLA	Guo, Bao-Zhu,et al."On exponential stability of a semilinear wave equation with variable coefficients under the nonlinear boundary feedback".NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 71.12(2009):5961-5978.