Determination of source terms in a degenerate parabolic equation from a locally distributed observation

Jacques Tort

doi:10.1016/j.crma.2010.10.031

Partial Differential Equations/Optimal Control

Determination of source terms in a degenerate parabolic equation from a locally distributed observation
[Détermination d'un terme source dans une équation parabolique dégénérée à partir d'une observation interne localisée]

Présenté par : Gilles Lebeau

Jacques Tort ¹

¹ Institut de mathématiques de Toulouse, UMR CNRS 5219, Université Paul-Sabatier Toulouse III, 118, route de Narbonne, 31 062 Toulouse cedex 4, France

Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1287-1291.

Résumé
Abstract

Le but de cette Note est de montrer un résultat d'unicité et stabilité pour un problème inverse consistant à déterminer un terme source dans une équation parabolique dégénérée en dimension 1. On reprend la méthode introduite par Imanuvilov et Yamamoto en 1998 en précisant une inégalité de Carleman récente obtenue par Cannarsa, Martinez et Vancostenoble.

The aim of this Note is to prove a Lipschitz stability and uniqueness result for an inverse source problem relative to a one-dimensional degenerate parabolic equation. We use the method introduced by Imanuvilov and Yamamoto in 1998, with the help of some recent Carleman estimate for degenerate equations obtained by Cannarsa, Martinez and Vancostenoble.

Reçu le : 2010-03-09
Accepté le : 2010-10-25
Publié le : 2010-11-17

DOI : 10.1016/j.crma.2010.10.031

Affiliations des auteurs :

Jacques Tort ¹

¹ Institut de mathématiques de Toulouse, UMR CNRS 5219, Université Paul-Sabatier Toulouse III, 118, route de Narbonne, 31 062 Toulouse cedex 4, France

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     title = {Determination of source terms in a degenerate parabolic equation from a locally distributed observation},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1287--1291},
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     volume = {348},
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     year = {2010},
     doi = {10.1016/j.crma.2010.10.031},
     language = {en},
}

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Jacques Tort. Determination of source terms in a degenerate parabolic equation from a locally distributed observation. Comptes Rendus. Mathématique, Volume 348 (2010) no. 23-24, pp. 1287-1291. doi : 10.1016/j.crma.2010.10.031. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.10.031/

Bibliographie
Cité par

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[3] P. Cannarsa; P. Martinez; J. Vancostenoble Carleman estimates for a class of degenerate parabolic operators, SIAM J. Control Optim., Volume 47 (2008) no. 1, pp. 1-19

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[5] P. Cannarsa, J. Tort, M. Yamamoto, Determination of source terms in a degenerate parabolic equation, in preparation.

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[11] J. Vancostenoble Sharp Carleman estimates for singular parabolic equations and application to Lipschitz stability in inverse source problems, C. R. Acad. Sci. Paris, Ser. I, Volume 348 (2010), pp. 801-805

[12] M. Yamamoto; J. Zou Simultaneous reconstruction of the initial temperature and heat radiative coefficient, Inverse Problems, Volume 17 (2001) no. 4, pp. 1181-1202

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