Global attractor and its perturbations for a dissipative hyperbolic equation

We consider a dissipative hyperbolic equation with nonlinear term having hi gh degree of polynomial growth. In this case, the uniqueness theorem for th e corresponding Cauchy problem is not proved. For this equation we construc t the global attractor, study its properties, and prove that the global att ractors of the Galerkin approximation systems converge from below to the gl obal attractor of the original hyperbolic equation. We prove that the depen dence of global attractors of hyperbolic equations with rapidly oscillating spatial terms depend on the global attractor of the averaged equation is u pper semicontinuous as the oscillation frequency tends to infinity. Stronge r results are obtained for hyperbolic equations with moderate growth of non linear terms.