Boundary Controllability for the Quasilinear Wave Equation

doi:10.1007/s00245-009-9088-7

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	Boundary Controllability for the Quasilinear Wave Equation
	Yao, Peng-Fei
	2010-04-01
发表期刊	APPLIED MATHEMATICS AND OPTIMIZATION
ISSN	0095-4616
卷号	61 期号:2 页码:191-233
摘要	We study the boundary exact controllability for the quasilinear wave equation in high dimensions. Our main tool is the geometric analysis. We derive the existence of long time solutions near an equilibrium, prove the locally exact controllability around the equilibrium under some checkable geometrical conditions. We then establish the globally exact controllability in such a way that the state of the quasilinear wave equation moves from an equilibrium in one location to an equilibrium in another location under some geometrical conditions. The Dirichlet action and the Neumann action are studied, respectively. Our results show that exact controllability is geometrical characters of a Riemannian metric, given by the coefficients and equilibria of the quasilinear wave equation. A criterion of exact controllability is given, which based on the sectional curvature of the Riemann metric. Some examples are presented to verify the global exact controllability.
关键词	Quasi-linear wave equation Exact controllability Sectional curvature
DOI	10.1007/s00245-009-9088-7
语种	英语
资助项目	NNSF of China[60225003] ; NNSF of China[60334040] ; NNSF of China[60821091] ; NNSF of China[60774025] ; NNSF of China[10831007] ; NNSF of China[KJCX3-SYW-S01]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000273785900003
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10921
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 100190, Peoples R China
推荐引用方式 GB/T 7714	Yao, Peng-Fei. Boundary Controllability for the Quasilinear Wave Equation[J]. APPLIED MATHEMATICS AND OPTIMIZATION,2010,61(2):191-233.
APA	Yao, Peng-Fei.(2010).Boundary Controllability for the Quasilinear Wave Equation.APPLIED MATHEMATICS AND OPTIMIZATION,61(2),191-233.
MLA	Yao, Peng-Fei."Boundary Controllability for the Quasilinear Wave Equation".APPLIED MATHEMATICS AND OPTIMIZATION 61.2(2010):191-233.