Indirect stabilization of weakly coupled systems with hybrid boundary conditions

Fatiha Alabau-Boussouira; Piermarco Cannarsa; Roberto Guglielmi

doi:10.3934/mcrf.2011.1.413

Article Contents

2011, Volume 1, Issue 4: 413-436. Doi: 10.3934/mcrf.2011.1.413

This issue Previous Article Next Article Pathwise Taylor expansions for Itô random fields

Indirect stabilization of weakly coupled systems with hybrid boundary conditions

1.
Present position Délégation CNRS at MAPMO, UMR 6628, Current position Université Paul Verlaine-Metz, Ile du Saulcy, 57045 Metz Cedex 1
2.
Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133 Roma
3.
Dipartimento di Matematica - Università di Roma "Tor Vergata", Via della Ricerca Scientifica 1 - 00133 Roma

Received: March 2011

Revised: July 2011

Published: December 2011

Abstract / Introduction Related Papers Cited by

Abstract

We investigate stability properties of indirectly damped systems of evolution equations in Hilbert spaces, under new compatibility assumptions. We prove polynomial decay for the energy of solutions and optimize our results by interpolation techniques, obtaining a full range of power-like decay rates. In particular, we give explicit estimates with respect to the initial data. We discuss several applications to hyperbolic systems with hybrid boundary conditions, including the coupling of two wave equations subject to Dirichlet and Robin type boundary conditions, respectively.

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Mathematics Subject Classification: 93D15, 35L53, 47D06, 46B70.

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