Global attractor for a composite system of nonlinear wave and plate equations

Francesca Bucci; Igor Chueshov; Irena Lasiecka

doi:10.3934/cpaa.2007.6.113

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2007, Volume 6, Issue 1: 113-140. Doi: 10.3934/cpaa.2007.6.113

This issue Previous Article Periodic solutions of nonlinear periodic differential systems with a small parameter Next Article Some nonexistence results for quasilinear PDE's

Global attractor for a composite system of nonlinear wave and plate equations

1.
Università degli Studi di Firenze, Dipartimento di Matematica Applicata, Via S. Marta 3, 50139 Firenze
2.
Kharkov University, Department of Mathematics and Mechanics, 4 Svobody sq, 61077 Kharkov
3.
University of Virginia, Department of Mathematics, Charlottesville, VA 22901

Received: February 28, 2006

Revised: June 30, 2006

Published: February 2007

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Abstract

We prove the existence of a compact, finite dimensional, global attractor for a system of strongly coupled wave and plate equations with nonlinear dissipation and forces. This kind of models describes fluid-structure interactions. Though our main focus is on the composite system of two partial differential equations, the result achieved yields as well a new contribution to the asymptotic analysis of either (uncoupled) equation.

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Mathematics Subject Classification: Primary: 37L30, 35M20; Secondary: 74H40.

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