An inverse problem of radiative potentials and initial temperatures in parabolic equations with dynamic boundary conditions

We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations with dynamic boundary conditions. We prove a Lipschitz stability estimate for the relevant potentials using a recent Carleman est...

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Bibliographic Details
Published inJournal of inverse and ill-posed problems Vol. 30; no. 3; pp. 363 - 378
Main Authors Ait Ben Hassi, El Mustapha, Chorfi, Salah-Eddine, Maniar, Lahcen
Format Journal Article
LanguageEnglish
Published Berlin De Gruyter 01.06.2022
Walter de Gruyter GmbH
Subjects
35K57
35R30
Boundary conditions
Carleman estimate
Convexity
dynamic boundary conditions
Dynamic stability
Inverse problem
Inverse problems
Lipschitz stability
logarithmic stability
Mathematical analysis
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Summary:We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations with dynamic boundary conditions. We prove a Lipschitz stability estimate for the relevant potentials using a recent Carleman estimate, and a logarithmic stability result for the initial temperatures by a logarithmic convexity method, based on observations in an arbitrary subdomain.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0928-0219
1569-3945
DOI:10.1515/jiip-2020-0067