A weighted identity for partial differential operators of second order and its applications

Xiaoyu Fu

doi:10.1016/j.crma.2006.02.023

Optimal Control

A weighted identity for partial differential operators of second order and its applications
[Une identité avec poids pour des opérateurs aux dérivées partielles du second ordre et ses applications]

Présenté par : Philippe G. Ciarlet

Xiaoyu Fu ¹

¹ School of Mathematics, Sichuan University, Chengdu 610064, China

Comptes Rendus. Mathématique, Volume 342 (2006) no. 8, pp. 579-584.

Résumé
Abstract

Dans cette Note, nous établissons une identité avec poids pour des opérateurs aux dérivées partielles du second ordre. De cette égalité, découlent tous les resultats connus de contrôlabilité/observabilité pour les équations paraboliques, les équations hyperboliques, l'équation de Schrödinger et celle des plaques, tous obtenus à partir des inégalités de Carleman. Par ailleurs, un nouveau résultat de contrôlabilité/observabilité est obtenu pour les équations de type paraboliques avec des coefficients à valeur complexe.

In this Note, a weighted identity for partial differential operators of second order is established. As its applications, one may deduce all the known controllability/observability results for the parabolic, hyperbolic, Schrödinger and plate equations that are derived via Carleman estimate. Meanwhile, a new controllability/observability result is presented for the parabolic equations with a complex principal part.

Reçu le : 2005-08-08
Accepté le : 2006-02-21
Publié le : 2006-03-20

DOI : 10.1016/j.crma.2006.02.023

Affiliations des auteurs :

Xiaoyu Fu ¹

¹ School of Mathematics, Sichuan University, Chengdu 610064, China

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Xiaoyu Fu. A weighted identity for partial differential operators of second order and its applications. Comptes Rendus. Mathématique, Volume 342 (2006) no. 8, pp. 579-584. doi : 10.1016/j.crma.2006.02.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2006.02.023/

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