Indirect stabilization of weakly coupled systems with hybrid boundary conditions

Fatiha Alabau-Boussouira; Piermarco Cannarsa; Roberto Guglielmi

hal-00601281, version 1

Indirect stabilization of weakly coupled systems with hybrid boundary conditions

Fatiha Alabau-Boussouira ^1, 2, Piermarco Cannarsa () ³, Roberto Guglielmi ³

(2011)

Résumé : 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.

1 : Laboratoire de Mathématiques et Applications de Metz (LMAM)
CNRS : UMR7122 – Université Paul Verlaine - Metz
2 : CORIDA (INRIA Nancy - Grand Est / IECN / LMAM)
INRIA – CNRS : UMR7502 – Université de Lorraine
3 : Dipartimento di Matematica [Roma II] (DIPMAT)
Universita degli studi di Roma Tor Vergata

Collaboration : CORIDA

hal-00601281, version 1
http://hal.archives-ouvertes.fr/hal-00601281
oai:hal.archives-ouvertes.fr:hal-00601281
Contributeur : Fatiha Alabau-Boussouira <>
Soumis le : Vendredi 17 Juin 2011, 11:44:39
Dernière modification le : Vendredi 17 Juin 2011, 15:08:34

Voir la fiche détaillée

Documents associés

PDF :

Exporter

Bibtex EndNote TEI RefWorks

<?xml version="1.0" encoding="UTF-8"?>
<listBibl xmlns="http://www.tei-c.org/ns/1.0" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<listBibl type="article"><head>Documents sans référence de publication (Preprint)</head>
<biblStruct type="article" xml:id="hal-00601281"><analytic>
<author><persName><forename>Fatiha</forename><surname>Alabau-Boussouira</surname></persName>
<affiliation>
<orgName type="laboratory">LMAM</orgName>
<orgName type="team">Laboratoire de Mathématiques et Applications de Metz</orgName>
<country>FR</country>
<orgName type="institution">CNRS : UMR7122</orgName>
<orgName type="institution">Université Paul Verlaine - Metz</orgName>
</affiliation>
<affiliation>
<orgName type="laboratory">INRIA Nancy - Grand Est / IECN / LMAM</orgName>
<orgName type="team">CORIDA</orgName>
<country>FR</country>
<orgName type="institution">INRIA</orgName>
<orgName type="institution">CNRS : UMR7502</orgName>
<orgName type="institution">Université de Lorraine</orgName>
</affiliation>
</author>
<author><persName><forename>Piermarco</forename><surname>Cannarsa</surname></persName>
<affiliation>
<orgName type="laboratory">DIPMAT</orgName>
<orgName type="team">Dipartimento di Matematica [Roma II]</orgName>
<country>IT</country>
<orgName type="institution">Universita degli studi di Roma Tor Vergata</orgName>
</affiliation>
</author>
<author><persName><forename>Roberto</forename><surname>Guglielmi</surname></persName>
<affiliation>
<orgName type="laboratory">DIPMAT</orgName>
<orgName type="team">Dipartimento di Matematica [Roma II]</orgName>
<country>IT</country>
<orgName type="institution">Universita degli studi di Roma Tor Vergata</orgName>
</affiliation>
</author>
<title type="main" level="a">Indirect stabilization of weakly coupled systems with hybrid boundary conditions</title></analytic><monogr><imprint/></monogr><idno type="HALid">http://hal.archives-ouvertes.fr/hal-00601281</idno><idno type="HALFile">http://hal.archives-ouvertes.fr/hal-00601281/PDF/1106.0263v1-1.pdf</idno></biblStruct>
</listBibl>
</listBibl>