Comptes Rendus
Théorie du contrôle
Reachable states for the distributed control of the heat equation
Mo Chen1 ; Lionel Rosier2
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.

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.

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DOI : 10.5802/crmath.310
Classification : 35K40, 93B05
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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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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