中国科学院机构知识库网格
Chinese Academy of Sciences Institutional Repositories Grid
首页 机构 成果 学者
  
  1. CAS IR Grid
  2. 数学与系统科学研究院
  3. 中国科学院数学与系统科学研究院
  4. 计算数学与科学工程计算研究所
PDE-CONSTRAINED OPTIMAL CONTROL APPROACH FOR THE APPROXIMATION OF AN INVERSE CAUCHY PROBLEM

文献类型：期刊论文

作者Chang, Lili1; Gong, Wei2; Sun, Guiquan1; Yan, Ningning3
刊名INVERSE PROBLEMS AND IMAGING
出版日期2015-08-01
卷号9期号:3页码:791-814
关键词Elliptic equation Cauchy problem Tikhonov regularization PDE-constrained optimal control finite element method
ISSN号1930-8337
DOI10.3934/ipi.2015.9.791
英文摘要This paper concerns the approximation of a Cauchy problem for the elliptic equation. The inverse problem is transformed into a PDE-constrained optimal control problem and these two problems are equivalent under some assumptions. Different from the existing literature which is also based on the optimal control theory, we consider the state equation in the sense of very weak solution defined by the transposition technique. In this way, it does not need to impose any regularity requirement on the given data. Moreover, this method can yield theoretical analysis simply and numerical computation conveniently. To deal with the ill-posedness of the control problem, Tikhonov regularization term is introduced. The regularized problem is well-posed and its solution converges to the non-regularized counterpart as the regularization parameter approaches zero. We establish the finite element approximation to the regularized control problem and the convergence of the discrete problem is also investigated. Then we discuss the first order optimality condition of the control problem further and obtain an efficient numerical scheme for the Cauchy problem via the adjoint state equation. The paper is ended with numerical experiments.
资助项目National Basic Research Program of China[2010CB731505] ; National Basic Research Program of China[2012CB821204] ; National Nature Science Foundation of China[11171337] ; National Nature Science Foundation of China[11201464]
WOS研究方向Mathematics ; Physics
语种英语
WOS记录号WOS:000360672300008
出版者AMER INST MATHEMATICAL SCIENCES
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/20710]  
专题计算数学与科学工程计算研究所
系统科学研究所
通讯作者Chang, Lili
作者单位1.Shanxi Univ, Complex Syst Res Ctr, Taiyuan 030006, Shanxi, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, LSEC,NCMIS, Beijing 100190, Peoples R China
推荐引用方式
GB/T 7714		 Chang, Lili,Gong, Wei,Sun, Guiquan,et al. PDE-CONSTRAINED OPTIMAL CONTROL APPROACH FOR THE APPROXIMATION OF AN INVERSE CAUCHY PROBLEM[J]. INVERSE PROBLEMS AND IMAGING,2015,9(3):791-814.
APA Chang, Lili,Gong, Wei,Sun, Guiquan,&Yan, Ningning.(2015).PDE-CONSTRAINED OPTIMAL CONTROL APPROACH FOR THE APPROXIMATION OF AN INVERSE CAUCHY PROBLEM.INVERSE PROBLEMS AND IMAGING,9(3),791-814.
MLA Chang, Lili,et al."PDE-CONSTRAINED OPTIMAL CONTROL APPROACH FOR THE APPROXIMATION OF AN INVERSE CAUCHY PROBLEM".INVERSE PROBLEMS AND IMAGING 9.3(2015):791-814.

入库方式： OAI收割

来源：数学与系统科学研究院

浏览0
下载0
收藏0
其他版本

除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。