Global smooth solutions for the quasilinear wave equation with boundary dissipation

doi:10.1016/j.jde.2007.06.014

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	Global smooth solutions for the quasilinear wave equation with boundary dissipation
	Yao, Peng-Fei
	2007-10-01
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	241 期号:1 页码:62-93
摘要	We consider the existence of global solutions of the quasilinear wave equation with a boundary dissipation structure of an input-output in high dimensions when initial data and boundary inputs are near a given equilibrium of the system. Our main tool is the geometrical analysis. The main interest is to study the effect of the boundary dissipation structure on solutions of the quasilinear system. We show that the existence of global solutions depends not only on this dissipation structure but also on a Riemannian metric, given by the coefficients and the equilibrium of the system. Some geometrical conditions on this Riemannian metric are presented to guarantee the existence of global solutions. In particular, we prove that the norm of the state of the system decays exponentially if the input stops after a finite time, which implies the exponential stabilization of the system by boundary feedback. (c) 2007 Elsevier Inc. All rights reserved.
关键词	quasilinear wave equation Riemannian metric dissipative boundary structure
DOI	10.1016/j.jde.2007.06.014
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000250232500003
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/4827
专题	系统科学研究所
通讯作者	Yao, Peng-Fei
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Control & Syst, Beijing 100081, Peoples R China
推荐引用方式 GB/T 7714	Yao, Peng-Fei. Global smooth solutions for the quasilinear wave equation with boundary dissipation[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2007,241(1):62-93.
APA	Yao, Peng-Fei.(2007).Global smooth solutions for the quasilinear wave equation with boundary dissipation.JOURNAL OF DIFFERENTIAL EQUATIONS,241(1),62-93.
MLA	Yao, Peng-Fei."Global smooth solutions for the quasilinear wave equation with boundary dissipation".JOURNAL OF DIFFERENTIAL EQUATIONS 241.1(2007):62-93.