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