Global attractors for the wave equation with nonlinear damping

Based on a new a priori estimate method, so-called asymptotic a priori estimate, the existence of a global attractor is proved for the wave equation utt+kg(ut)−Δu+f(u)=0 on a bounded domain with Dirichlet boundary conditions. The nonlinear damping term g is supposed to satisfy the growth condition C1(s−C2) g(s) C3(1+sp), where 1 p<5; the damping parameter is arbitrary; the nonlinear term f is supposed to satisfy the growth condition f′(s) C4(1+sq), where q 2. It is remarkable that when 2