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

Presented by: 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.

Abstract
Résumé

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.

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.

Received: 2005-08-08
Accepted: 2006-02-21
Published online: 2006-03-20

DOI: 10.1016/j.crma.2006.02.023

Author's affiliations:

Xiaoyu Fu ¹

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

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     title = {A weighted identity for partial differential operators of second order and its applications},
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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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