Point sources and stability for an inverse problem for a hyperbolic PDE with space and time dependent coefficients

We study stability aspects for the determination of space and time-dependent lower order perturbations of the wave operator in three space dimensions with point sources. The problems under consideration here are formally determined and we establish Lipschitz stability results for these problems. The...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 342; pp. 622 - 665
Main Authors Krishnan, Venkateswaran P., Rakesh, Senapati, Soumen
Format Journal Article
LanguageEnglish
Published Elsevier Inc 05.01.2023
Subjects
Carleman estimates
Formally determined hyperbolic inverse problem
Stability
Time dependent coefficients
35K20
Stability
35R30
35L05
Carleman estimates
Formally determined hyperbolic inverse problem
Time dependent coefficients
35L20
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Summary:We study stability aspects for the determination of space and time-dependent lower order perturbations of the wave operator in three space dimensions with point sources. The problems under consideration here are formally determined and we establish Lipschitz stability results for these problems. The main tool in our analysis is a modified version of Bukgheĭm-Klibanov method based on Carleman estimates.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2022.10.025