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Comptes Rendus Mathématique
Volume 353, n° 1
pages 63-68 (janvier 2015)
Doi : 10.1016/j.crma.2014.10.023
Received : 14 October 2014 ;  accepted : 23 October 2014
Critères du type de Kálmán pour la contrôlabilité approchée et la synchronisation approchée d'un système couplé d'équations des ondes
Criteria of Kálmán's type for the approximate controllability and the approximate synchronization of a coupled system of wave equations
 

Tatsien Li a, b, 1 , Bopeng Rao c
a School of Mathematical Sciences, Fudan University, Shanghai 200433, China 
b Shanghai Key Laboratory for Contemporary Applied Mathematics, Nonlinear Mathematical Modeling and Methods Laboratory, China 
c Institut de recherche mathématique avancée, Université de Strasbourg, 67084 Strasbourg, France 

Résumé

Dans cette Note, nous obtenons des conditions nécessaires, exprimées sous la forme de critères du type de Kálmán, pour la contrôlabilité nulle approchée et la synchronisation approchée par groupes d'un système couplé d'équations des ondes avec des contrôles frontières de Dirichlet. De plus, nous établissons la suffisance de ces conditions pour certains systèmes, en particulier pour des systèmes en dimension d'espace un.

The full text of this article is available in PDF format.
Abstract

In this Note, we obtain necessary conditions, formulated as criteria of Kálmán's type, for the approximate null controllability and the approximate synchronization by groups of a coupled system of wave equations with Dirichlet boundary controls. We also establish the sufficiency of these conditions for some systems, in particular for systems in one space dimension.

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1  Projet supporté par the National Basic Research Program of China (No. 2013CB834100), and the National Natural Science Foundation of China (No. 11121101).


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