Volume 17, Number 3, July-September 2011
|Page(s)||801 - 835|
|Published online||06 August 2010|
Logarithmic decay of the energy for an hyperbolic-parabolic coupled system
Laboratoire LMV, Université de Versailles
Saint-Quentin-en-Yvelines, 45 Avenue des États-Unis, Bâtiment Fermat,
78035 Versailles, France. firstname.lastname@example.org
Revised: 14 November 2009
Revised: 31 March 2010
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.
Mathematics Subject Classification: 37L15 / 35B37 / 74F10 / 93D20
Key words: Fluid-structure interaction / wave-heat model / stability / logarithmic decay
© EDP Sciences, SMAI, 2010
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