Logarithmic decay of the energy for an hyperbolic-parabolic coupled system
ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 3, pp. 801-835.

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.

DOI : 10.1051/cocv/2010026
Classification : 37L15, 35B37, 74F10, 93D20
Mots-clés : fluid-structure interaction, wave-heat model, stability, logarithmic decay 
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     title = {Logarithmic decay of the energy for an hyperbolic-parabolic coupled system},
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Fathallah, Ines Kamoun. Logarithmic decay of the energy for an hyperbolic-parabolic coupled system. ESAIM: Control, Optimisation and Calculus of Variations, Tome 17 (2011) no. 3, pp. 801-835. doi : 10.1051/cocv/2010026. http://archive.numdam.org/articles/10.1051/cocv/2010026/

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