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Comptes Rendus Mathématique
Volume 342, n° 11
pages 849-852 (juin 2006)
Doi : 10.1016/j.crma.2006.04.001
Received : 13 December 2005 ;  accepted : 30 Mars 2006
Application of the exact null controllability of the heat equation to moving sets
Application de la contrôlabilité exacte à zéro de lʼéquation de la chaleur au déplacement dʼensembles
 

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

Abstract

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. To cite this article: T. Horsin Molinaro, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

The full text of this article is available in PDF format.
Résumé

On étudie la contrôlabilité lagrangienne de lʼéquation de la chaleur en toutes dimensions. En dimension 1, on montre que deux intervalles quelconques sont difféomorphes via le flot de la solution de lʼéquation 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. Pour citer cet article : T. Horsin Molinaro, C. R. Acad. Sci. Paris, Ser. I 342 (2006).

The full text of this article is available in PDF format.
1  The author wishes to thank J.-P. Puel for suggesting him related problems.


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