TIME DISCRETE WAVE EQUATIONS: BOUNDARY OBSERVABILITY AND CONTROL

doi:10.3934/dcds.2009.23.571

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	TIME DISCRETE WAVE EQUATIONS: BOUNDARY OBSERVABILITY AND CONTROL
	Zhang, Xu 1,2; Zheng, Chuang 3; Zuazua, Enrique 4
	2009
发表期刊	DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
ISSN	1078-0947
卷号	23 期号:1-2 页码:571-604
摘要	In this paper we study the exact boundary controllability of a trapezoidal time discrete wave equation in a bounded domain. We prove that the projection of the solution in an appropriate filtered space is exactly controllable with uniformly bounded cost with respect to the time-step. In this way, the well-known exact-controllability property of the wave equation can be reproduced as the limit, as the time step h -> 0, of the controllability of projections of the time-discrete one. By duality these results are equivalent to deriving uniform observability estimates (with respect to h -> 0) within a class of solutions of the time-discrete problem in which the high frequency components have been filtered. The later is established by means of a time-discrete version of the classical multiplier technique. The optimality of the order of the filtering parameter is also established, although a careful analysis of the expected velocity of propagation of time-discrete waves indicates that its actual value could be improved.
关键词	Exact controllability observability time discretization wave equation multiplier technique filtering
DOI	10.3934/dcds.2009.23.571
语种	英语
资助项目	Spanish MEC[MTM2005-00714] ; MEC (Spain)[CIT-370200-2005-10] ; CAM (Spain) ; NSF of China[10525105]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000260923300031
出版者	AMER INST MATHEMATICAL SCIENCES
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7501
专题	中国科学院数学与系统科学研究院
通讯作者	Zhang, Xu
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Sichuan Univ, Yangtze Ctr Math, Chengdu 610064, Peoples R China 3.Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China 4.Basque Ctr Appl Math, Bilbao 48009, Spain
推荐引用方式 GB/T 7714	Zhang, Xu,Zheng, Chuang,Zuazua, Enrique. TIME DISCRETE WAVE EQUATIONS: BOUNDARY OBSERVABILITY AND CONTROL[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,2009,23(1-2):571-604.
APA	Zhang, Xu,Zheng, Chuang,&Zuazua, Enrique.(2009).TIME DISCRETE WAVE EQUATIONS: BOUNDARY OBSERVABILITY AND CONTROL.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS,23(1-2),571-604.
MLA	Zhang, Xu,et al."TIME DISCRETE WAVE EQUATIONS: BOUNDARY OBSERVABILITY AND CONTROL".DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS 23.1-2(2009):571-604.