KMS Of Academy of mathematics and systems sciences, CAS
| Time reversal focusing of the initial state for Kirchhoff plate | |
| Phung, Kim Dang1; Xu Zhang1,2 | |
| 2008 | |
| 发表期刊 | SIAM JOURNAL ON APPLIED MATHEMATICS
 |
| ISSN | 0036-1399 |
| 卷号 | 68期号:6页码:1535-1556 |
| 摘要 | Consider a Kirchhoff plate partial derivative(2)(t)u + Delta(2)u - partial derivative(2)(t)Delta u = 0 in Omega x (0, T), with boundary data u = Delta u = 0 on partial derivative Omega x (0, T) and unknown initial data u(., 0) = u(0) and partial derivative(t)u(., 0) = u(1) in Omega. We study an inverse problem of determining (u(0), u(1)) from an interior observation u vertical bar(w) x(0, T). Here Omega is a bounded domain,. a nonempty open subset of Omega, and T > 0 a suitable time duration. By means of an iterative time reversal technique, we derive an asymptotic formula of reconstructing ( u0, u1) approximately with a logarithmical convergence rate for smooth initial data. The convergence becomes uniform and exponential when (Omega, w, T) satisfies the geometric control condition introduced by Bardos, Lebeau, and Rauch. |
| 关键词 | Kirchhoff plate inverse problem quantitative unique continuation observability estimate time reversal technique |
| DOI | 10.1137/070684823 |
| 语种 | 英语 |
| 资助项目 | NSF of China[10525105] ; NSF of China[10771149] ; Spanish MEC[MTM2005-00714] ; Chinese Postdoctoral Science Foundation |
| WOS研究方向 | Mathematics |
| WOS类目 | Mathematics, Applied |
| WOS记录号 | WOS:000258894800003 |
| 出版者 | SIAM PUBLICATIONS |
| 引用统计 | |
| 文献类型 | 期刊论文 |
| 条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/5903 |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Phung, Kim Dang |
| 作者单位 | 1.Sichuan Univ, Yangtze Ctr Math, Chengdu 610064, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100080, Peoples R China |
| 推荐引用方式 GB/T 7714 | Phung, Kim Dang,Xu Zhang. Time reversal focusing of the initial state for Kirchhoff plate[J]. SIAM JOURNAL ON APPLIED MATHEMATICS,2008,68(6):1535-1556. |
| APA | Phung, Kim Dang,&Xu Zhang.(2008).Time reversal focusing of the initial state for Kirchhoff plate.SIAM JOURNAL ON APPLIED MATHEMATICS,68(6),1535-1556. |
| MLA | Phung, Kim Dang,et al."Time reversal focusing of the initial state for Kirchhoff plate".SIAM JOURNAL ON APPLIED MATHEMATICS 68.6(2008):1535-1556. |
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