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

Ines Kamoun Fathallah

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 3, page 801-835
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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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 17.3 (2011): 801-835. <http://eudml.org/doc/272877>.

@article{Fathallah2011,
abstract = {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.},
author = {Fathallah, Ines Kamoun},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {fluid-structure interaction; wave-heat model; stability; logarithmic decay},
language = {eng},
number = {3},
pages = {801-835},
publisher = {EDP-Sciences},
title = {Logarithmic decay of the energy for an hyperbolic-parabolic coupled system},
url = {http://eudml.org/doc/272877},
volume = {17},
year = {2011},
}

TY - JOUR
AU - Fathallah, Ines Kamoun
TI - Logarithmic decay of the energy for an hyperbolic-parabolic coupled system
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2011
PB - EDP-Sciences
VL - 17
IS - 3
SP - 801
EP - 835
AB - 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.
LA - eng
KW - fluid-structure interaction; wave-heat model; stability; logarithmic decay
UR - http://eudml.org/doc/272877
ER -

References

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  12. [12] J. Rauch, X. Zhang and E. Zuazua, Polynomial decay for a hyperbolic-parabolic coupled system. J. Math. Pures Appl.84 (2005) 407–470. Zbl1077.35030MR2132724
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