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Logarithmic decay of the energy for an hyperbolic-parabolic coupled system

Published online by Cambridge University Press:  06 August 2010

Ines Kamoun Fathallah
Ines Kamoun Fathallah*
Affiliation:
Laboratoire LMV, Université de Versailles Saint-Quentin-en-Yvelines, 45 Avenue des États-Unis, Bâtiment Fermat, 78035 Versailles, France. ines.fathallah@math.uvsq.fr
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Abstract

This paper is devoted to the study of a coupled system which consists of a wave equation and a heat equation coupled through a transmission condition along a steady interface. This system is a linearized model for fluid-structure interaction introduced by Rauch, Zhang and Zuazua for a simple transmission condition and by Zhang and Zuazua for a natural transmission condition. Using an abstract theorem of Burq and a new Carleman estimate proved near the interface, we complete the results obtained by Zhang and Zuazua and by Duyckaerts. We prove, without a Geometric Control Condition, a logarithmic decay of the energy.

Keywords

Fluid-structure interactionwave-heat modelstabilitylogarithmic decay
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 17 , Issue 3 , July 2011 , pp. 801 - 835
Copyright
© EDP Sciences, SMAI, 2010

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