Logarithmic decay of the energy for an hyperbolic-parabolic coupled system
Ines Kamoun Fathallah (LM-Versailles)
TL;DR
This paper proves a logarithmic decay of energy in a coupled wave and heat system with transmission conditions, extending previous results through new estimates and without geometric restrictions.
Contribution
It introduces a new Carleman estimate near the interface and completes existing decay results for the coupled system without geometric constraints.
Findings
Logarithmic decay of energy established
New Carleman estimate near the interface
Extension of previous results without geometric restrictions
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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