A new Carleman inequality for parabolic systems with a single observation and applications

Assia Benabdallah; Michel Cristofol; Patricia Gaitan; Luz de Teresa

doi:10.1016/j.crma.2009.11.001

Partial Differential Equations/Optimal Control

A new Carleman inequality for parabolic systems with a single observation and applications
[Une nouvelle inégalité de Carleman pour des systèmes paraboliques avec une seule observation et applications]

Présenté par : Gilles Lebeau

Assia Benabdallah ¹ ; Michel Cristofol ¹ ; Patricia Gaitan ¹ ; Luz de Teresa ²

¹ Laboratoire d'analyse topologie probabilités, CNRS UMR 6632, universités d'Aix-Marseille, 39, rue F. Joliot Curie 1, 13453 Marseille cedex 13, France
² Instituto de Matemáticas, Universidad Nacional Autónoma de México

Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 25-29.

Résumé
Abstract

On établit des inégalités d'observabilité pour des systèmes linéaires de réaction–diffusion–convection d'ordre 2 et des systèmes linéaires de réaction–diffusion d'ordre 3, basées sur des estimations de Carleman. Elles permettent de démontrer des résultats de contrôlabilité aux trajectoires par une seule force localisée en espace ainsi que des résultats d'identification de n coefficients par $(n - 2)$ observations.

In this Note, we present Carleman estimates for linear reaction–diffusion–convection systems of two equations and linear reaction–diffusion systems of three equations. These estimates are the key for proving controllability results for semilinear reaction–diffusion–convection systems of order 2 and reaction–diffusion systems of order 3. They allow us to derive results for identification of n coefficients by $(n - 2)$ observations.

Reçu le : 2009-06-18
Accepté le : 2009-11-02
Publié le : 2010-01-01

DOI : 10.1016/j.crma.2009.11.001

Affiliations des auteurs :

Assia Benabdallah ¹ ; Michel Cristofol ¹ ; Patricia Gaitan ¹ ; Luz de Teresa ²

¹ Laboratoire d'analyse topologie probabilités, CNRS UMR 6632, universités d'Aix-Marseille, 39, rue F. Joliot Curie 1, 13453 Marseille cedex 13, France
² Instituto de Matemáticas, Universidad Nacional Autónoma de México

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     author = {Assia Benabdallah and Michel Cristofol and Patricia Gaitan and Luz de Teresa},
     title = {A new {Carleman} inequality for parabolic systems with a single observation and applications},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {25--29},
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     year = {2010},
     doi = {10.1016/j.crma.2009.11.001},
     language = {en},
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Assia Benabdallah; Michel Cristofol; Patricia Gaitan; Luz de Teresa. A new Carleman inequality for parabolic systems with a single observation and applications. Comptes Rendus. Mathématique, Volume 348 (2010) no. 1-2, pp. 25-29. doi : 10.1016/j.crma.2009.11.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.11.001/

Bibliographie
Cité par

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