Geodesic
Partial Differential Equations/Optimal Control
Controllability of the Ginzburg–Landau equation
[Contrôlabilité de l'équation de Ginzburg–Landau]

Présenté par : Haïm Brezis

Rosier, Lionel1, 2 ; Zhang, Bing-Yu3
1 Centro de Modelamiento Matemático (CMM) and Departamento de Ingeniería Matemática, Universidad de Chile (UMI CNRS 2807), Avenida Blanco Encalada 2120, Casilla 170-3, Correo 3, Santiago, Chile
2 Institut Élie-Cartan, UMR 7502 UHP/CNRS/INRIA, B.P. 239, 54506 Vandoeuvre-lès-Nancy cedex, France
3 Department of Mathematical Sciences, University of Cincinnati,Cincinnati, OH 45221, USA
Comptes Rendus. Mathématique, Tome 346 (2008) no. 3-4, pp. 167-172.

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This Note investigates the boundary controllability, as well as the internal controllability, of the complex Ginzburg–Landau equation. Null-controllability results are derived from a Carleman estimate and an analysis based upon the theory of sectorial operators.

Cette Note est dévolue à l'étude de la contrôlabilité frontière, ou interne, de l'équation complexe de Ginzburg–Landau. Des résultats de contrôlabilité à zéro sont obtenus au moyen d'une inégalité de Carleman et d'une analyse basée sur la théorie des opérateurs sectoriels.

Accepté le :
Publié le :
DOI : 10.1016/j.crma.2007.11.031

Rosier, Lionel 1, 2 ; Zhang, Bing-Yu 3

1 Centro de Modelamiento Matemático (CMM) and Departamento de Ingeniería Matemática, Universidad de Chile (UMI CNRS 2807), Avenida Blanco Encalada 2120, Casilla 170-3, Correo 3, Santiago, Chile
2 Institut Élie-Cartan, UMR 7502 UHP/CNRS/INRIA, B.P. 239, 54506 Vandoeuvre-lès-Nancy cedex, France
3 Department of Mathematical Sciences, University of Cincinnati,Cincinnati, OH 45221, USA 
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Rosier, Lionel; Zhang, Bing-Yu. Controllability of the Ginzburg–Landau equation. Comptes Rendus. Mathématique, Tome 346 (2008) no. 3-4, pp. 167-172. doi : 10.1016/j.crma.2007.11.031. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2007.11.031/

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