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

Ines Kamoun Fathallah (1)

1 LMV - Laboratoire de Mathématiques de Versailles

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.

Mots clés: Fluid-structure interaction; Wave-heat model; Stability; Logarithmic decay.; Logarithmic decay

Domaines: Equations aux dérivées partielles [math.AP]

Ines Kamoun Fathallah. Logarithmic decay of the energy for an hyperbolic-parabolic coupled system. 2009. ⟨hal-00397336⟩