Logarithmic decay of the energy for an hyperbolic-parabolic coupled system
ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 3, p. 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 : https://doi.org/10.1051/cocv/2010026
Classification:  37L15,  35B37,  74F10,  93D20
Keywords: fluid-structure interaction, wave-heat model, stability, logarithmic decay
@article{COCV_2011__17_3_801_0,
     author = {Fathallah, Ines Kamoun},
     title = {Logarithmic decay of the energy for an hyperbolic-parabolic coupled system},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {17},
     number = {3},
     year = {2011},
     pages = {801-835},
     doi = {10.1051/cocv/2010026},
     zbl = {1223.37098},
     mrnumber = {2826981},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2011__17_3_801_0}
}
Fathallah, Ines Kamoun. Logarithmic decay of the energy for an hyperbolic-parabolic coupled system. ESAIM: Control, Optimisation and Calculus of Variations, Volume 17 (2011) no. 3, pp. 801-835. doi : 10.1051/cocv/2010026. http://www.numdam.org/item/COCV_2011__17_3_801_0/

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