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

2009/06/23 by Fathallah, Ines Kamoun
#35B37 #37L15 #74F10 #93D20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0906.4178

Abstract

This paper is devoted to the study of a coupled system consisting in a wave and heat equations coupled through 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 shown near the interface, we complete the results obtained by Zhang and Zuazua and by Duyckaerts. We show, without any geometric restriction, a logarithmic decay result.

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