Minimal time of controllability of two parabolic equations with disjoint control and coupling domains

Farid Ammar Khodja; Assia Benabdallah; Manuel González-Burgos; Luz de Teresa

doi:10.1016/j.crma.2014.03.004

Partial differential equations/Optimal control

Minimal time of controllability of two parabolic equations with disjoint control and coupling domains
[Temps minimal de contrôlabilité de deux équations paraboliques avec des domaines de contrôle et de couplage disjoints]

Présenté par : Gilles Lebeau

Farid Ammar Khodja ¹ ; Assia Benabdallah ² ; Manuel González-Burgos ³ ; Luz de Teresa ⁴

¹ Laboratoire de mathématiques de Besançon, université de Franche-Comté, 16, route de Gray, 25030 Besançon cedex, France
² Aix–Marseille Université, CNRS, Centrale Marseille, l2M, UMR 7373, 13453 Marseille, France
³ Dpto. E.D.A.N., Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain
⁴ Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U. 04510 D.F., Mexico

Comptes Rendus. Mathématique, Volume 352 (2014) no. 5, pp. 391-396.

Résumé
Abstract

On considère deux équations paraboliques couplées par une matrice $A (x) = q (x) A_{0}$ , où $A_{0}$ est un bloc de Jordan d'ordre 1, et contrôlées par un seul contrôle localisé en espace ou frontière. Le support du coefficient de couplage, q, et celui du contrôle peuvent être disjoints. Nous mettons en évidence un temps minimal de contrôlabilité à 0, $T_{0} (q) \in [0, + \infty]$ .

We consider two parabolic equations coupled by a matrix $A (x) = q (x) A_{0}$ , where $A_{0}$ is a Jordan block of order 1, and controlled by a single localized function, or by a single boundary control. The support of the coupling coefficient, q, and the control domain may be disjoint. We exhibit an explicit minimal time of null-controllability, $T_{0} (q) \in [0, + \infty]$ .

Reçu le : 2014-01-10
Accepté le : 2014-03-05
Publié le : 2014-04-03

DOI : 10.1016/j.crma.2014.03.004

Affiliations des auteurs :

Farid Ammar Khodja ¹ ; Assia Benabdallah ² ; Manuel González-Burgos ³ ; Luz de Teresa ⁴

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     author = {Farid Ammar Khodja and Assia Benabdallah and Manuel Gonz\'alez-Burgos and Luz de Teresa},
     title = {Minimal time of controllability of two parabolic equations with disjoint control and coupling domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {391--396},
     publisher = {Elsevier},
     volume = {352},
     number = {5},
     year = {2014},
     doi = {10.1016/j.crma.2014.03.004},
     language = {en},
}

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Farid Ammar Khodja; Assia Benabdallah; Manuel González-Burgos; Luz de Teresa. Minimal time of controllability of two parabolic equations with disjoint control and coupling domains. Comptes Rendus. Mathématique, Volume 352 (2014) no. 5, pp. 391-396. doi : 10.1016/j.crma.2014.03.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.03.004/

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