Controllability and observability of a heat equation with hyperbolic memory kernel

doi:10.1016/j.jde.2009.07.026

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	Controllability and observability of a heat equation with hyperbolic memory kernel
	Fu, Xiaoyu 2; Yong, Jiongmin 3,4; Zhang, Xu 1,5
	2009-10-15
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	247 期号:8 页码:2395-2439
摘要	The exact controllability and observability for a heat equation with hyperbolic memory kernel in anisotropic and nonhomogeneous media are considered. Due to the appearance of such a kind of memory, the speed of propagation for solutions to the heat equation is finite and the corresponding controllability property has a certain nature similar to hyperbolic equations, and is significantly different from that of the usual parabolic equations. By means of Carleman estimate, we establish a positive controllability and observability result under some geometric condition. On the other hand, by a careful construction of highly concentrated approximate solutions to hyperbolic equations with memory, we present a negative controllability and observability result when the geometric condition is not satisfied. (C) 2009 Elsevier Inc. All rights reserved.
关键词	Heat equation with memory Controllability Observability estimate Carleman estimate Highly concentrated approximate solution
DOI	10.1016/j.jde.2009.07.026
语种	英语
资助项目	NSFC[10525105] ; NSFC[10831007] ; NSFC[60821091] ; NSF[DMS-0604309] ; Chunhui program (State Education Ministry of China)[Z007-1-61006] ; Spanish Ministry of Science and Innovation[MTM2008-03541]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000270563900010
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/7557
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, Key Lab Syst & Control, Beijing 100190, Peoples R China 2.Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China 3.Univ Cent Florida, Dept Math, Orlando, FL 32816 USA 4.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China 5.Sichuan Univ, Yangtze Ctr Math, Chengdu 610064, Peoples R China
推荐引用方式 GB/T 7714	Fu, Xiaoyu,Yong, Jiongmin,Zhang, Xu. Controllability and observability of a heat equation with hyperbolic memory kernel[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2009,247(8):2395-2439.
APA	Fu, Xiaoyu,Yong, Jiongmin,&Zhang, Xu.(2009).Controllability and observability of a heat equation with hyperbolic memory kernel.JOURNAL OF DIFFERENTIAL EQUATIONS,247(8),2395-2439.
MLA	Fu, Xiaoyu,et al."Controllability and observability of a heat equation with hyperbolic memory kernel".JOURNAL OF DIFFERENTIAL EQUATIONS 247.8(2009):2395-2439.