On the controllability for Maxwell's equations in specific media

Patrick Courilleau; Thierry Horsin Molinaro

doi:10.1016/j.crma.2005.10.011

Optimal Control

On the controllability for Maxwell's equations in specific media

Presented by: Philippe G. Ciarlet

Patrick Courilleau ¹; Thierry Horsin Molinaro ²

¹ Université de Cergy-Pontoise, département de mathématiques (UMR 8088), 2, avenue Adophe-Chauvin, 95302 Cergy-Pontoise cedex, France
² Université de Versailles-St Quentin, laboratoire de mathématiques appliquées, 45, avenue des États-Unis, 78035 Versailles, France

Comptes Rendus. Mathématique, Volume 341 (2005) no. 11, pp. 665-668.

Abstract
Résumé

In this Note we study the problem of exact controllability of the Maxwell's equations in specific media with two different models, on the one hand the so-called Drude–Born–Fedorov model, in the time domain, and on the other hand a simplified bilinear medium.

For the first one we prove the non approximate controllability whereas for the second one we are able to prove the exact controllability under the usual conditions of the wave equation.

Dans cette Note nous étudions le problème de la contrôlabilité exacte des équations de Maxwell en milieux spécifiques avec deux différents modèles, d'un côté le modèle en temps de Drude–Born–Fedorov, et d'un autre côté un milieu bilinéaire simplifié.

Pour le premier on prouve la non contrôlabilité approchée alors que pour le second nous prouvons la contrôlabilité exacte sous les conditions usuelles suffisantes de l'équation des ondes.

Received: 2005-06-28
Accepted: 2005-10-11
Published online: 2005-11-10

DOI: 10.1016/j.crma.2005.10.011

Author's affiliations:

Patrick Courilleau ¹; Thierry Horsin Molinaro ²

¹ Université de Cergy-Pontoise, département de mathématiques (UMR 8088), 2, avenue Adophe-Chauvin, 95302 Cergy-Pontoise cedex, France
² Université de Versailles-St Quentin, laboratoire de mathématiques appliquées, 45, avenue des États-Unis, 78035 Versailles, France

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     author = {Patrick Courilleau and Thierry Horsin Molinaro},
     title = {On the controllability for {Maxwell's} equations in specific media},
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     doi = {10.1016/j.crma.2005.10.011},
     language = {en},
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Patrick Courilleau; Thierry Horsin Molinaro. On the controllability for Maxwell's equations in specific media. Comptes Rendus. Mathématique, Volume 341 (2005) no. 11, pp. 665-668. doi : 10.1016/j.crma.2005.10.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.10.011/

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