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Comptes Rendus Mathématique
Volume 350, n° 9-10
pages 493-498 (mai 2012)
Doi : 10.1016/j.crma.2012.04.003
Received : 5 December 2011 ;  accepted : 4 April 2012
Stabilisation faible interne locale de système élastique de Bresse
Weakly locally internal stabilization of elastic Bresse system
 

Nahla Noun a, b, 1 , Ali Wehbe a, 2
a Equipe EDP et analyse numérique, université libanaise, faculté des sciences 1 et EDST & Hadath, Beyrouth, Liban 
b Université Montpellier 2, ACSIOM, place Eugène-Bataillon, 34095 Montpellier, France 

Résumé

Dans [[1]], Alabau-Boussouira et al. (2011) ont étudié la stabilisation exponentielle et polynomiale de système de Bresse sous lʼaction dʼune seule loi de dissipation interne globalement distribuée. Dans cette Note, notre but est dʼétendre les résultats de Alabau-Boussouira et al. (2011) [[1]], pour prendre en considération le cas important où la loi de dissipation est localement distribuée et pour améliorer le taux de décroissance polynomial de lʼénergie. Nous étudions alors, le taux de décroissance de lʼénergie du système de Bresse sous lʼaction dʼune seule loi de dissipation interne localement distribuée et agissant sur lʼéquation de rotation angulaire. Sous la condition dʼégalité des vitesses de propagation, nous montrons que le système est exponentiellement stable. Dans le cas contraire, nous établissons un nouveau taux de décroissance polynomial de lʼénergie.

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Abstract

In [[1]], Alabau-Boussouira et al. (2011) studied the exponential and polynomial stability of the Bresse system with one globally distributed dissipation law. In this Note, our goal is to extend the results from Alabau-Boussouira et al. (2011) [[1]], by taking into consideration the important case when the dissipation law is locally distributed and to improve the polynomial energy decay rate. We then study the energy decay rate of the Bresse system with one locally internal distributed dissipation law acting on the equation about the shear angle displacement. Under the equal speed wave propagation condition, we show that the system is exponentially stable. On the contrary, we establish a new polynomial energy decay rate.

The full text of this article is available in PDF format.
1  La thèse de doctorat de N. Noun est financée par lʼassociation Azm et Saadé, Liban.
2  Projet de recherche UL, Dossier 20654.


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