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
[Contrôlabilité de l'équation de Ginzburg–Landau]

Présenté par : 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.

Résumé
Abstract

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.

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.

Accepté le : 2007-11-21
Publié le : 2007-12-26

DOI : 10.1016/j.crma.2007.11.031

Affiliations des auteurs :

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},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {167--172},
     publisher = {Elsevier},
     volume = {346},
     number = {3-4},
     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/

Bibliographie
Cité par

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