Stability for inverse source problems by Carleman estimates

In this article, we provide a modified argument for proving stability for inverse problems of determining spatially varying functions in evolution equations by Carleman estimates. Our method does not require any cut-off procedures and therefore simplifies the existing proofs. We establish the condit...

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Bibliographic Details
Published inInverse problems Vol. 36; no. 12; pp. 125006 - 125025
Main Authors Huang, X, Yu Imanuvilov, O, Yamamoto, M
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.12.2020
Subjects
Carleman estimate
inverse source problem
stability
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ISSN0266-5611
1361-6420
DOI10.1088/1361-6420/aba892

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Summary:In this article, we provide a modified argument for proving stability for inverse problems of determining spatially varying functions in evolution equations by Carleman estimates. Our method does not require any cut-off procedures and therefore simplifies the existing proofs. We establish the conditional stability for inverse source problems for a hyperbolic equation and a parabolic equation, and our method is widely applicable to various evolution equations.
Bibliography:IP-102635.R1
ISSN:0266-5611
1361-6420
DOI:10.1088/1361-6420/aba892