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Global smooth solutions of the quasi-linear wave equation with internal velocity feedback
Zhang, Zhi-Fei; Yao, Peng-Fei
2008
Source PublicationSIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN0363-0129
Volume47Issue:4Pages:2044-2077
AbstractWe 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.
Keywordquasi-linear wave equation Riemannian metric internal velocity feedback
DOI10.1137/070679454
Language英语
Funding ProjectNational 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 Research AreaAutomation & Control Systems ; Mathematics
WOS SubjectAutomation & Control Systems ; Mathematics, Applied
WOS IDWOS:000258895300017
PublisherSIAM PUBLICATIONS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/5524
Collection系统科学研究所
Corresponding AuthorZhang, Zhi-Fei
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100080, Peoples R China
Recommended Citation
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.
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