Asymptotic analysis of a simple model of fluid-structure interaction

Serge Nicaise; Cristina Pignotti

doi:10.3934/nhm.2008.3.787

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2008, Volume 3, Issue 4: 787-813. Doi: 10.3934/nhm.2008.3.787

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Asymptotic analysis of a simple model of fluid-structure interaction

Serge Nicaise^1, and
Cristina Pignotti^2,

1.
Université de Valenciennes et du Hainaut Cambrésis, LAMAV and FR CNRS 2956, Le Mont Houy, Institut des Sciences et Techniques de Valenciennes, 59313 Valenciennes Cedex 9
2.
Dipartimento di Matematica Pura e Applicata, Università di L'Aquila, Via Vetoio, Loc. Coppito, 67010 L'Aquila

Received: February 29, 2008

Revised: March 31, 2008

Published: November 2008

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Abstract

This paper is devoted to the asymptotic analysis of simple models of fluid-structure interaction, namely a system between the heat and wave equations coupled via some transmission conditions at the interface. The heat part induces the dissipation of the full system. Here we are interested in the behavior of the model when the thickness of the heat part and/or the heat diffusion coefficient go to zero or to infinity. The limit problem is a wave equation with a boundary condition at the interface, this boundary condition being different according to the limit of the above mentioned parameters. It turns out that some limit problems are dissipative but some of them are non dissipative or their behavior is unknown.

Keywords:

Fluid-structure system,
asympotic behavior.

Mathematics Subject Classification: 35B30, 35M10, 35B40, 93D20.

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