Asymptotic analysis of a simple model of fluid-structure interaction

Pages: 787 - 813, Volume 3, Issue 4, December 2008

doi:10.3934/nhm.2008.3.787       Abstract        Full Text (310.3K)       Related Articles

Serge Nicaise - Université de Valenciennes et du Hainaut Cambrésis, LAMAV and FR CNRS 2956, Institut des Sciences et Techniques de Valenciennes, 59313 Valenciennes Cedex 9, France (email)
Cristina Pignotti - Dipartimento di Matematica Pura e Applicata, Università di L'Aquila, Via Vetoio, Loc. Coppito, 67010 L'Aquila, Italy (email)

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

Received: March 2008;      Revised: April 2008;      Published: October 2008.