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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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1569-3945
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Volume 25, Issue 1

Issues

Reciprocity gap method for an interior inverse scattering problem

Fang Zeng
  • Corresponding author
  • Institute of Computing and Data Sciences, College of Mathematics and Statistics, Chongqing University, 400044 Chongqing, P. R. China; and Postdoctoral Station of Optical Engineering, Chongqing University, 401331 Chongqing, P. R. China
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/ Xiaodong Liu / Jiguang Sun / Liwei Xu
  • Institute of Computing and Data Sciences, College of Mathematics and Statistics, Chongqing University, 400044 Chongqing, P. R. China
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Published Online: 2016-01-28 | DOI: https://doi.org/10.1515/jiip-2015-0064

Abstract

We consider an interior inverse scattering problem of reconstructing the shape of a cavity with inhomogeneous medium inside. We prove a uniqueness theorem for the inverse problem. Using Cauchy data on a curve inside the cavity due to interior point sources, we employ the reciprocity gap method to reconstruct the cavity. Numerical examples are provided to show the effectiveness of the method.

Keywords: Interior inverse scattering; inhomogeneous medium; Dirichlet eigenvalue; reciprocity gap method

MSC 2010: 45Q05

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About the article

Received: 2015-06-15

Revised: 2015-11-13

Accepted: 2015-12-12

Published Online: 2016-01-28

Published in Print: 2017-02-01


The work of Fang Zeng was supported by Chongqing Postdoctoral Research Project Special Fund with project No. Xm2014081 and the Fundamental Research Funds for the Central Universities with project No. CDJZR14105501. The research of Xiaodong Liu was supported in part by the NNSF of China under grant 11101412 and the National Center for Mathematics and Interdisciplinary Sciences, CAS. The research of Jiguang Sun was partially supported by all MTU REF grant and NSF CNIC-1427665. The work of Liwei Xu was partially supported by the NSFC grant 11371385, the Start-up Fund of Youth 1000 Plan of China and that of Youth 100 Plan of Chongqing University.


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 25, Issue 1, Pages 57–68, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2015-0064.

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