An inverse problem for a hyperbolic system in a bounded domain

Laure Cardoulis

doi:10.5802/crmath.431

Théorie du contrôle

An inverse problem for a hyperbolic system in a bounded domain
[Un problème inverse pour un système hyperbolique dans un domaine borné]

Laure Cardoulis ¹

¹ Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France.

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 653-665.

Résumé
Abstract

Dans cette Note, on considère un système hyperbolique de deux équations, défini dans un domaine borné. En utilisant la méthode des inégalités de Carleman, on obtient un résultat de stabilité Lipschitz pour les quatre coefficients dépendant de la variable d’espace de ce système, avec des mesures d’une seule composante de la solution et grâce à la donnée de deux ensembles de conditions initiales.

In this Note we consider a two-by-two hyperbolic system defined on a bounded domain. Using Carleman inequalities, we obtain a Lipschitz stability result for the four spatially varying coefficients with measurements of only one component, given two sets of initial conditions.

Reçu le : 2022-06-30
Révisé le : 2022-09-22
Accepté le : 2022-09-27
Publié le : 2023-03-02

DOI : 10.5802/crmath.431

Classification : 35R30

Affiliations des auteurs :

Laure Cardoulis ¹

¹ Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France.

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {An inverse problem for a hyperbolic system in a bounded domain},
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     doi = {10.5802/crmath.431},
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Laure Cardoulis. An inverse problem for a hyperbolic system in a bounded domain. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 653-665. doi : 10.5802/crmath.431. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.431/

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