Application of the exact null controllability of the heat equation to moving sets

Thierry Horsin Molinaro

doi:10.1016/j.crma.2006.04.001

Partial Differential Equations

Application of the exact null controllability of the heat equation to moving sets
[Application de la contrôlabilité exacte à zéro de l'équation de la chaleur au déplacement d'ensembles]

Présenté par : Gilles Lebeau

Thierry Horsin Molinaro ¹

¹ Université de Versailles-Saint Quentin, laboratoire de mathématiques appliquées, 45, avenue de États-Unis, 78030 Versailles cedex, France

Comptes Rendus. Mathématique, Volume 342 (2006) no. 11, pp. 849-852.

Résumé
Abstract

On étudie la contrôlabilité lagrangienne de l'équation de la chaleur en toutes dimensions. En dimension 1, on montre que deux intervalles quelconques sont difféomorphes via le flot de la solution de l'équation de la chaleur avec un contrôle adéquat. En dimension supérieure on prouve un résultat de contrôlabilité similaire pour le flot du gradient, en temps fini fixé pour le cas radial, et en temps assez grand pour le cas convexe.

We study the lagrangian controllability of the heat equation in several dimensions. In dimension one, we prove that any pairs of intervals are diffeomorphic through the flow of the solution of the heat equation via an adequate control. In higher dimensions we prove a similar controllability result for the flow of the gradient of the solution in a radial case in arbitrary finite time, and for convex domains in a sufficiently large time.

Reçu le : 2005-12-13
Accepté le : 2006-03-30
Publié le : 2006-05-03

DOI : 10.1016/j.crma.2006.04.001

Affiliations des auteurs :

Thierry Horsin Molinaro ¹

¹ Université de Versailles-Saint Quentin, laboratoire de mathématiques appliquées, 45, avenue de États-Unis, 78030 Versailles cedex, France

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     language = {en},
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Thierry Horsin Molinaro. Application of the exact null controllability of the heat equation to moving sets. Comptes Rendus. Mathématique, Volume 342 (2006) no. 11, pp. 849-852. doi : 10.1016/j.crma.2006.04.001. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.04.001/

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