# American Institute of Mathematical Sciences

March  2007, 6(1): 113-140. doi: 10.3934/cpaa.2007.6.113

## 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, Italy 2 Kharkov University, Department of Mathematics and Mechanics, 4 Svobody sq, 61077 Kharkov 3 University of Virginia, Department of Mathematics, Charlottesville, VA 22901

Received  March 2006 Revised  July 2006 Published  December 2006

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.
Citation: Francesca Bucci, Igor Chueshov, Irena Lasiecka. Global attractor for a composite system of nonlinear wave and plate equations. Communications on Pure & Applied Analysis, 2007, 6 (1) : 113-140. doi: 10.3934/cpaa.2007.6.113
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