Controllability of the Ginzburg–Landau equation

Lionel Rosier; Bing-Yu Zhang

doi:10.1016/j.crma.2007.11.031

Partial Differential Equations/Optimal Control

Controllability of the Ginzburg–Landau equation

Presented by: Haïm Brezis

Lionel Rosier ^1,²; Bing-Yu Zhang 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

Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 167-172.

Abstract
Résumé

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.

Accepted: 2007-11-21
Published online: 2007-12-26

DOI: 10.1016/j.crma.2007.11.031

Author's affiliations:

Lionel Rosier ^{1, 2}; Bing-Yu Zhang 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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     author = {Lionel Rosier and Bing-Yu Zhang},
     title = {Controllability of the {Ginzburg{\textendash}Landau} equation},
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     pages = {167--172},
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     year = {2008},
     doi = {10.1016/j.crma.2007.11.031},
     language = {en},
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Lionel Rosier; Bing-Yu Zhang. Controllability of the Ginzburg–Landau equation. Comptes Rendus. Mathématique, Volume 346 (2008) no. 3-4, pp. 167-172. doi : 10.1016/j.crma.2007.11.031. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2007.11.031/

References
Cited by

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