Stabilization of locally coupled wave-type systems
Résumé
In this paper, we consider a system of two wave equations on a bounded domain, 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.
Domaines
Analyse numérique [cs.NA]
Origine : Fichiers produits par l'(les) auteur(s)
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