Reachable states for the distributed control of the heat equation

Mo Chen; Lionel Rosier

doi:10.5802/crmath.310

Théorie du contrôle

Reachable states for the distributed control of the heat equation

Mo Chen ¹ ; Lionel Rosier ²

¹ School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, 130024, P. R. China
² Université du Littoral Côte d’Opale, Laboratoire de Mathématiques Pures et Appliquées J. Liouville, BP 699, F-62228 Calais, France

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 627-639.

Résumé

We are concerned with the determination of the reachable states for the distributed control of the heat equation on an interval. We consider either periodic boundary conditions or homogeneous Dirichlet boundary conditions. We prove that for a $L^{2}$ distributed control, the reachable states are in the Sobolev space $H^{1}$ and that they have complex analytic extensions on squares whose horizontal diagonals are regions where no control is applied.

Reçu le : 2021-06-25
Révisé le : 2021-11-12
Accepté le : 2021-12-07
Publié le : 2022-06-22

Zbl

DOI : 10.5802/crmath.310

Classification : 35K40, 93B05

Affiliations des auteurs :

Mo Chen ¹ ; Lionel Rosier ²

¹ School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, 130024, P. R. China
² Université du Littoral Côte d’Opale, Laboratoire de Mathématiques Pures et Appliquées J. Liouville, BP 699, F-62228 Calais, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Reachable states for the distributed control of the heat equation},
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Mo Chen; Lionel Rosier. Reachable states for the distributed control of the heat equation. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 627-639. doi : 10.5802/crmath.310. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.310/

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