Finite-Dimensionality of Attractors Associated with von Kármán Plate Equations and Boundary Damping

Asymptotic behavior of solutions to a fully nonlinear von Kármán system is considered. The existence of compact attractors in the presence of nonlinear boundary damping is established. It is also shown that in the case of linear boundary dissipation, this attractor is of finite Hausdorff dimension (with explicit estimates of the dimension).