Controllability and observability of a heat equation with hyperbolic memory kernel
文献类型：期刊论文
| 作者 | Fu, Xiaoyu2; Yong, Jiongmin3,4; Zhang, Xu1,5 |
| 刊名 | JOURNAL OF DIFFERENTIAL EQUATIONS
 |
| 出版日期 | 2009-10-15 |
| 卷号 | 247期号:8页码:2395-2439 |
| 关键词 | Heat equation with memory Controllability Observability estimate Carleman estimate Highly concentrated approximate solution |
| ISSN号 | 0022-0396 |
| DOI | 10.1016/j.jde.2009.07.026 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000270563900010 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/7556]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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