Global smooth solutions of the quasi-linear wave equation with internal velocity feedback

doi:10.1137/070679454

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	Global smooth solutions of the quasi-linear wave equation with internal velocity feedback
	Zhang, Zhi-Fei; Yao, Peng-Fei
	2008
发表期刊	SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN	0363-0129
卷号	47 期号:4 页码:2044-2077
摘要	We study the existence of global smooth solutions for the quasi-linear wave equation by an internal local damping when initial data are close to a given equilibrium. Our interest is in studying the structure of the damping region, which guarantees the existence of global solutions. Our results show that the structure of the damping region depends on the geometric properties of a Riemannian metric, based on the coefficients and the equilibrium of the system. Some geometrical conditions are presented to obtain the damping region.
关键词	quasi-linear wave equation Riemannian metric internal velocity feedback
DOI	10.1137/070679454
语种	英语
资助项目	National Natural Science Foundation of China[60225003] ; National Natural Science Foundation of China[60334040] ; National Natural Science Foundation of China[60221301] ; National Natural Science Foundation of China[60774025]
WOS研究方向	Automation & Control Systems ; Mathematics
WOS类目	Automation & Control Systems ; Mathematics, Applied
WOS记录号	WOS:000258895300017
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5524
专题	系统科学研究所
通讯作者	Zhang, Zhi-Fei
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Zhang, Zhi-Fei,Yao, Peng-Fei. Global smooth solutions of the quasi-linear wave equation with internal velocity feedback[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,2008,47(4):2044-2077.
APA	Zhang, Zhi-Fei,&Yao, Peng-Fei.(2008).Global smooth solutions of the quasi-linear wave equation with internal velocity feedback.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,47(4),2044-2077.
MLA	Zhang, Zhi-Fei,et al."Global smooth solutions of the quasi-linear wave equation with internal velocity feedback".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 47.4(2008):2044-2077.