Indirect controllability of locally coupled systems under geometric conditions

Fatiha Alabau-Boussouira; Matthieu Léautaud

doi:10.1016/j.crma.2011.02.004

Partial Differential Equations/Optimal Control

Indirect controllability of locally coupled systems under geometric conditions

Presented by: Jean-Michel Bony

Fatiha Alabau-Boussouira ¹; Matthieu Léautaud ^2,^3,⁴

¹ Université Paul Verlaine-Metz, Metz Cedex 1, France
² Université Pierre-et-Marie-Curie, Paris 6, UMR 7598, Laboratoire Jacques-Louis-Lions, 75005 Paris, France
³ CNRS, UMR 7598 LJLL, 75005 Paris, France
⁴ Laboratoire POEMS, INRIA Paris-Rocquencourt/ENSTA, CNRS UMR 2706, 78153 Le Chesnay, France

Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 395-400.

Abstract
Résumé

We consider systems of two wave/heat/Schrödinger-type equations coupled by a zero order term, only one of them being controlled. We prove an internal and a boundary null-controllability result in any space dimension, provided that both the coupling and the control regions satisfy the Geometric Control Condition. This includes several examples in which these two regions have an empty intersection.

On sʼintéresse à des systèmes constitués de deux équations dʼondes, de la chaleur ou de Schrödinger, couplées par un terme dʼordre zéro, et dont seulement lʼune est controlée. En supposant que les zones de couplage et de contrôle satisfont toutes deux la Condition Géométrique de Contrôle, on montre un résultat de contrôle interne et frontière en dimension quelconque dʼespace. Ceci fournit de nombreux exemples pour lesquels ces deux régions ne sʼintersectent pas.

Received: 2010-12-09
Accepted: 2011-02-03
Published online: 2011-02-26

DOI: 10.1016/j.crma.2011.02.004

Author's affiliations:

Fatiha Alabau-Boussouira ¹; Matthieu Léautaud ^{2, 3, 4}

¹ Université Paul Verlaine-Metz, Metz Cedex 1, France
² Université Pierre-et-Marie-Curie, Paris 6, UMR 7598, Laboratoire Jacques-Louis-Lions, 75005 Paris, France
³ CNRS, UMR 7598 LJLL, 75005 Paris, France
⁴ Laboratoire POEMS, INRIA Paris-Rocquencourt/ENSTA, CNRS UMR 2706, 78153 Le Chesnay, France

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     author = {Fatiha Alabau-Boussouira and Matthieu L\'eautaud},
     title = {Indirect controllability of locally coupled systems under geometric conditions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {395--400},
     publisher = {Elsevier},
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     number = {7-8},
     year = {2011},
     doi = {10.1016/j.crma.2011.02.004},
     language = {en},
}

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Fatiha Alabau-Boussouira; Matthieu Léautaud. Indirect controllability of locally coupled systems under geometric conditions. Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 395-400. doi : 10.1016/j.crma.2011.02.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.02.004/

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