On the boundary controllability of non-scalar parabolic systems

Enrique Fernández-Cara; Manuel González-Burgos; Luz de Teresa

doi:10.1016/j.crma.2009.04.020

Partial Differential Equations

On the boundary controllability of non-scalar parabolic systems
[Sur la contrôlabilité frontière des systèmes paraboliques non scalaires]

Présenté par : Gilles Lebeau

Enrique Fernández-Cara ¹ ; Manuel González-Burgos ¹ ; Luz de Teresa ²

¹ Dpto. E.D.A.N., Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain
² Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U. 04510 D.F., Mexico

Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 763-766.

Résumé
Abstract

Cette Note concerne la contrôlabilité frontière des systèmes paraboliques linéaires non scalaires. Plus précisement, on considère un système de deux équations paraboliques linéaires de dimension 1 en espace. Nous montrons qu'il est beaucoup plus compliqué de contrôler sur une partie du bord que de le faire avec des contrôles distribués. Dans notre résultat principal, on donne des conditions nécessaires et suffisantes pour la contrôlabilité exacte à zéro.

This Note is concerned with the boundary controllability of non-scalar linear parabolic systems. More precisely, two coupled one-dimensional linear parabolic equations are considered. We show that, with boundary controls, the situation is much more complex than for similar distributed control systems. In our main result, we provide necessary and sufficient conditions for null controllability.

Reçu le : 2009-03-10
Accepté le : 2009-04-16
Publié le : 2009-05-17

DOI : 10.1016/j.crma.2009.04.020

Affiliations des auteurs :

Enrique Fernández-Cara ¹ ; Manuel González-Burgos ¹ ; Luz de Teresa ²

¹ Dpto. E.D.A.N., Universidad de Sevilla, Aptdo. 1160, 41080 Sevilla, Spain
² Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U. 04510 D.F., Mexico

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     author = {Enrique Fern\'andez-Cara and Manuel Gonz\'alez-Burgos and Luz de Teresa},
     title = {On the boundary controllability of non-scalar parabolic systems},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {763--766},
     publisher = {Elsevier},
     volume = {347},
     number = {13-14},
     year = {2009},
     doi = {10.1016/j.crma.2009.04.020},
     language = {en},
}

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Enrique Fernández-Cara; Manuel González-Burgos; Luz de Teresa. On the boundary controllability of non-scalar parabolic systems. Comptes Rendus. Mathématique, Volume 347 (2009) no. 13-14, pp. 763-766. doi : 10.1016/j.crma.2009.04.020. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.04.020/

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