Controllability of cascade coupled systems of multi-dimensional evolution PDEs by a reduced number of controls

Fatiha Alabau-Boussouira

doi:10.1016/j.crma.2012.05.009

Partial Differential Equations/Optimal Control

Controllability of cascade coupled systems of multi-dimensional evolution PDEs by a reduced number of controls
[Contrôlabilité de systèmes multi-dimensionnels couplés en cascade par un nombre réduit de contrôles]

Présenté par : Jean-Michel Bony

Fatiha Alabau-Boussouira ¹

¹ LMAM CNRS-UMR 7122 et INRIA Equipe-projet CORIDA, Université de Lorraine, Ile du Saulcy, 57045 Metz cedex 01, France

Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 577-582.

Résumé
Abstract

Nous démontrons quʼil est possible de contrôler des systèmes de N équations dʼévolution faiblement couplées en cascade par un nombre réduit de contrôles frontière ou localement distribués, le nombre de contrôle pouvant varier de 1 à $N - 1$ . Nous donnons des applications aux systèmes couplés multi-dimensionnels en cascade hyperboliques, paraboliques et de Schrödinger.

We prove controllability results for abstract systems of weakly coupled N evolution equations in cascade by a reduced number of boundary or locally distributed controls ranging from a single up to $N - 1$ controls. We give applications to cascade coupled systems of N multi-dimensional hyperbolic, parabolic and diffusive equations.

Reçu le : 2011-08-04
Accepté le : 2012-05-21
Publié le : 2012-06-01

DOI : 10.1016/j.crma.2012.05.009

Affiliations des auteurs :

Fatiha Alabau-Boussouira ¹

¹ LMAM CNRS-UMR 7122 et INRIA Equipe-projet CORIDA, Université de Lorraine, Ile du Saulcy, 57045 Metz cedex 01, France

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     author = {Fatiha Alabau-Boussouira},
     title = {Controllability of cascade coupled systems of multi-dimensional evolution {PDEs} by a reduced number of controls},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {577--582},
     publisher = {Elsevier},
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     year = {2012},
     doi = {10.1016/j.crma.2012.05.009},
     language = {en},
}

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Fatiha Alabau-Boussouira. Controllability of cascade coupled systems of multi-dimensional evolution PDEs by a reduced number of controls. Comptes Rendus. Mathématique, Volume 350 (2012) no. 11-12, pp. 577-582. doi : 10.1016/j.crma.2012.05.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.05.009/

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