Simultaneous control for the heat equation with Dirichlet and Neumann boundary conditions
It is well known that both the heat equation with Dirichlet or Neumann boundary conditions are null controlable as soon as the control acts in a non trivial domain (i.e. a set of positive measure). In this article, we show that for any couple of initial data $(u_0, v_0)$ we can achieve the null cont...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.535/ |
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| author | Burq, Nicolas Moyano, Ivan |
| author_facet | Burq, Nicolas Moyano, Ivan |
| author_sort | Burq, Nicolas |
| collection | DOAJ |
| description | It is well known that both the heat equation with Dirichlet or Neumann boundary conditions are null controlable as soon as the control acts in a non trivial domain (i.e. a set of positive measure). In this article, we show that for any couple of initial data $(u_0, v_0)$ we can achieve the null control for both equations (Dirichlet and Neumann boundary conditions respectively) simultaneously with the same control function for both equations. |
| format | Article |
| id | doaj-art-278867f822d3499785bef6d36d1c119e |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-278867f822d3499785bef6d36d1c119e2025-02-07T11:23:07ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G993794210.5802/crmath.53510.5802/crmath.535Simultaneous control for the heat equation with Dirichlet and Neumann boundary conditionsBurq, Nicolas0Moyano, Ivan1Université Paris-Saclay, Mathématiques, UMR 8628 du CNRS, Bât 307, 91405 Orsay Cedex, France, and Institut Universitaire de FranceUniversité de Nice Sophia-Antipolis Parc Valrose, Laboratoire J.A. Dieudonné, UMR 7351 du CNRS 06108 Nice Cedex 02 FranceIt is well known that both the heat equation with Dirichlet or Neumann boundary conditions are null controlable as soon as the control acts in a non trivial domain (i.e. a set of positive measure). In this article, we show that for any couple of initial data $(u_0, v_0)$ we can achieve the null control for both equations (Dirichlet and Neumann boundary conditions respectively) simultaneously with the same control function for both equations.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.535/ |
| spellingShingle | Burq, Nicolas Moyano, Ivan Simultaneous control for the heat equation with Dirichlet and Neumann boundary conditions Comptes Rendus. Mathématique |
| title | Simultaneous control for the heat equation with Dirichlet and Neumann boundary conditions |
| title_full | Simultaneous control for the heat equation with Dirichlet and Neumann boundary conditions |
| title_fullStr | Simultaneous control for the heat equation with Dirichlet and Neumann boundary conditions |
| title_full_unstemmed | Simultaneous control for the heat equation with Dirichlet and Neumann boundary conditions |
| title_short | Simultaneous control for the heat equation with Dirichlet and Neumann boundary conditions |
| title_sort | simultaneous control for the heat equation with dirichlet and neumann boundary conditions |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.535/ |
| work_keys_str_mv | AT burqnicolas simultaneouscontrolfortheheatequationwithdirichletandneumannboundaryconditions AT moyanoivan simultaneouscontrolfortheheatequationwithdirichletandneumannboundaryconditions |