Controllability of some coupled parabolic systems by one control force

Manuel González-Burgos; Rosario Pérez-García

doi:10.1016/j.crma.2004.11.025

Partial Differential Equations/Optimal Control

Controllability of some coupled parabolic systems by one control force
[Contrôlabilité de quelques systèmes paraboliques couplés avec un seul contrôle]

Présenté par : Gilles Lebeau

Manuel González-Burgos ¹ ; Rosario Pérez-García ¹

¹ EDAN, Facultad de Matemáticas, Universidad de Sevilla, Apartado 1160, 41080 Sevilla, Spain

Comptes Rendus. Mathématique, Volume 340 (2005) no. 2, pp. 125-130.

Résumé
Abstract

Dans cette Note, on présente une nouvelle approche qui permet de prouver de nouveaux résultats de contrôlabilité pour quelques systèmes paraboliques couplés considerés dans un domaine borné Ω de $R^{N}$ et contrôlés par un seul contrôle distribué. On analyse, comme exemple modèle, la contrôlabilité nulle d'un système linéaire de champ de phases. D'abord, on contrôle le système par deux contrôles. Ensuite, on élimine le contrôle artificiel introduit. Des estimations globales de Carleman et la régularité parabolique sont employées.

In this Note we present a new approach which allows one to prove new controllability results for some coupled parabolic systems considered in a bounded domain Ω of $R^{N}$ when one controls by a unique distributed control. We analyze, as a model example, the null controllability of a linear phase field system. First, one controls the system by two controls. Then, one eliminates the introduced fictitious control. Global Carleman estimates and the parabolic regularity are used.

Reçu le : 2004-10-26
Accepté le : 2004-11-24
Publié le : 2004-12-22

DOI : 10.1016/j.crma.2004.11.025

Affiliations des auteurs :

Manuel González-Burgos ¹ ; Rosario Pérez-García ¹

¹ EDAN, Facultad de Matemáticas, Universidad de Sevilla, Apartado 1160, 41080 Sevilla, Spain

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     author = {Manuel Gonz\'alez-Burgos and Rosario P\'erez-Garc{\'\i}a},
     title = {Controllability of some coupled parabolic systems by one control force},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {125--130},
     publisher = {Elsevier},
     volume = {340},
     number = {2},
     year = {2005},
     doi = {10.1016/j.crma.2004.11.025},
     language = {en},
}

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Manuel González-Burgos; Rosario Pérez-García. Controllability of some coupled parabolic systems by one control force. Comptes Rendus. Mathématique, Volume 340 (2005) no. 2, pp. 125-130. doi : 10.1016/j.crma.2004.11.025. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.11.025/

Bibliographie
Cité par

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[2] O. Bodart; M. González-Burgos; R. Pérez-García Insensitizing controls for a semilinear heat equation with a superlinear nonlinearity, C. R. Acad. Sci. Paris, Volume 335 (2002) no. 8, pp. 677-682

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[5] M. González-Burgos, R. Pérez-García, Controllability results for some nonlinear coupled parabolic systems by one control force, in preparation

[6] M. González-Burgos, R. Pérez-García, Controllability of some nonlinear coupled parabolic systems by one control force in unbounded domains, in preparation

[7] R. Pérez-García, Thesis, Universidad de Sevilla, Sevilla, Spain, 2004

[8] E. Zuazua Exact controllability for the semilinear wave equation, J. Math. Pures Appl., Volume 69 (1990) no. 1, pp. 1-31

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