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hal-00476250, version 1

Stabilization of locally coupled wave-type systems

Fatiha Alabau-Boussouira 1, Matthieu Léautaud () 2

(03/2010)

Résumé : In this paper, we consider a system of two wave equations on a bounded domain $\Omega \subset \real^N$, that are coupled by a localized zero order term. Only one of the two equations is supposed to be damped. We show that the energy of smooth solutions of this system decays polynomially at infinity. This result is proved in an abstract setting for coupled second order evolution equations and is then applied to internal and boundary damping for wave and for plate systems. In one space dimension, this yields polynomial stability for any non-empty open coupling and damping regions, in particular if these two regions have empty intersection.

  • 1 :  Laboratoire de Mathématiques et Applications de Metz (LMAM)
  • CNRS : UMR7122 – Université Paul Verlaine - Metz
  • 2 :  Laboratoire Jacques-Louis Lions (LJLL)
  • CNRS : UMR7598 – Université Pierre et Marie Curie [UPMC] - Paris VI
  • Domaine : Mathématiques/Equations aux dérivées partielles
  • Mots-clés : Stabilization – Indirect damping – Hyperbolic systems – Wave equation
  • Versions disponibles :  v1 (29-04-2010) v2 (27-03-2011)
 
  • hal-00476250, version 1
  • http://hal.archives-ouvertes.fr/hal-00476250
  • oai:hal.archives-ouvertes.fr:hal-00476250
  • Contributeur : Matthieu Léautaud <>
  • Soumis le : Dimanche 25 Avril 2010, 16:49:26
  • Dernière modification le : Jeudi 29 Avril 2010, 08:17:01