A spectral inequality for degenerate operators and applications

Rémi Buffe; Kim Dang Phung

doi:10.1016/j.crma.2018.11.004

Partial differential equations

A spectral inequality for degenerate operators and applications
[Une inégalité spectrale pour les opérateurs dégénérés et applications]

Présenté par : Jean-Michel Coron

Rémi Buffe ¹ ; Kim Dang Phung ²

¹ Université de Lorraine, CNRS, Inria, IECL, F-54000 Nancy, France
² Institut Denis-Poisson, CNRS, UMR 7013, Université d'Orléans, BP 6759, 45067 Orléans cedex 2, France

Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1131-1155.

Résumé
Abstract

Dans cet article, on s'intéresse à l'inégalité spectrale de type Lebeau–Robbiano sur la somme de fonctions propres pour une famille d'opérateurs dégénérés. Les applications sont données en théorie du contrôle, comme le contrôle impulsionnel et la stabilisation en temps fini.

In this paper, we establish a Lebeau–Robbiano spectral inequality for a degenerate one-dimensional elliptic operator, and we show how it can be used to study impulse control and finite-time stabilization for a degenerate parabolic equation.

Reçu le : 2018-03-15
Accepté le : 2018-11-07
Publié le : 2018-11-01

DOI : 10.1016/j.crma.2018.11.004

Affiliations des auteurs :

Rémi Buffe ¹ ; Kim Dang Phung ²

¹ Université de Lorraine, CNRS, Inria, IECL, F-54000 Nancy, France
² Institut Denis-Poisson, CNRS, UMR 7013, Université d'Orléans, BP 6759, 45067 Orléans cedex 2, France

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     title = {A spectral inequality for degenerate operators and applications},
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     pages = {1131--1155},
     publisher = {Elsevier},
     volume = {356},
     number = {11-12},
     year = {2018},
     doi = {10.1016/j.crma.2018.11.004},
     language = {en},
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Rémi Buffe; Kim Dang Phung. A spectral inequality for degenerate operators and applications. Comptes Rendus. Mathématique, Volume 356 (2018) no. 11-12, pp. 1131-1155. doi : 10.1016/j.crma.2018.11.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.11.004/

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