Stable determination of coefficients in semilinear parabolic system with dynamic boundary conditions

In this work, we study the stable determination of four space-dependent coefficients appearing in a coupled semilinear parabolic system with variable diffusion matrices subject to dynamic boundary conditions which couple intern-boundary phenomena. We prove a Lipschitz stability result for interior a...

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Bibliographic Details
Published inInverse problems Vol. 38; no. 11; pp. 115007 - 115034
Main Authors Ait Ben Hassi, El Mustapha, Chorfi, Salah-Eddine, Maniar, Lahcen
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.11.2022
Subjects
Carleman estimate
dynamic boundary conditions
inverse problem
Lipschitz stability
observability
semilinear parabolic systems
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ISSN0266-5611
1361-6420
DOI10.1088/1361-6420/ac91ed

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Summary:In this work, we study the stable determination of four space-dependent coefficients appearing in a coupled semilinear parabolic system with variable diffusion matrices subject to dynamic boundary conditions which couple intern-boundary phenomena. We prove a Lipschitz stability result for interior and boundary potentials by means of only one observation component, localized in any arbitrary open subset of the physical domain. The proof mainly relies on some new Carleman estimates for dynamic boundary conditions of surface diffusion type.
Bibliography:IP-103467.R1
ISSN:0266-5611
1361-6420
DOI:10.1088/1361-6420/ac91ed