Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations

We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove Lipschitz stability estimates which ensure unique reconstruction of both coefficients. Our theoretical results are justified by numerical studies on the reconstruction of two unknown coefficients using noisy backscattered data. © 2017 IOP Publishing Ltd.

Authors
Beilina L.1 , Cristofol M.2 , Li S.3 , Yamamoto M. 4, 5
Journal
Inverse Problems
Publisher
Institute of Physics Publishing
Number of issue
1
Language
English
Status
Published
Link
External link
DOI
10.1088/1361-6420/aa941d
Number
015001
Volume
34
Year
2018
Organizations
  • 1 Department of Mathematical Sciences, Chalmers University of Technology, University of Gothenburg, Gothenburg, SE-42196, Sweden
  • 2 Institut de Mathématiques de Marseille, CNRS, UMR 7373, École Centrale, Aix-Marseille Université, Marseille, 13453, France
  • 3 Key Laboratory of Wu Wen-Tsun Mathematics, USTC, Chinese Academy of Sciences, School of Mathematical Sciences, University of Science, Technology of China, 96 Jinzhai Road, Anhui Province, Hefei, 230026, China
  • 4 Department of Mathematical Sciences, University of Tokyo, Komaba, Meguro, Tokyo, 153, Japan
  • 5 Research Center Center of Nonlinear Problems of Mathematical Physics, Peoples' Friendship University of Russia, 6 Miklucho-Maklaya, Moscow, 117198, Russian Federation
Keywords
adaptive algorithm; an acoustic equation of hyperbolic type; Carleman estimate; coefficient inverse problem; two space-dependent coefficients
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/7405/
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