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

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 :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.10.031

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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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/

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