American Institute of Mathematical Sciences

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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

Francesca Bucci 1, , Igor Chueshov 2, and  Irena Lasiecka 3,

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.
Keywords: wave-plate model, critical exponents., nonlinear damping, finite fractal dimension, Global attractor.
Mathematics Subject Classification: Primary: 37L30, 35M20; Secondary: 74H4.
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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