Boundary Controllability for the Quasilinear Wave Equation

doi:10.1007/s00245-009-9088-7

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 系统科学研究所

	Boundary Controllability for the Quasilinear Wave Equation
	Yao, Peng-Fei
刊名	APPLIED MATHEMATICS AND OPTIMIZATION
	2010-04-01
卷号	61 期号:2 页码:191-233
关键词	Quasi-linear wave equation Exact controllability Sectional curvature
ISSN号	0095-4616
DOI	10.1007/s00245-009-9088-7
英文摘要	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.
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000273785900003
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/10920]
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.