Long-time behaviour of nonlinearly damped semilinear wave equation

We present a new approach for proving of existence and finite-dimensionality of global attractors for infinite-dimensional dissipative systems generated by abstract nonlinear second order in time evolution equations. This approach is based on far reaching generalizations of the Ceron-Lopes theorem on asymptotic compactness and Ladyzhenskaya's theorem on the dimension of invariant sets. An application of our results to nonlinear damped wave equations allow us to obtain new results pertaining to structure and properties of global attractors for nonlinear waves.