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 Ω⊂R3 with Dirichlet boundary conditions. The nonlinear damping term g is supposed to satisfy the growth condition C1(|s|−C2)⩽|g(s)|⩽C3(1+|s|p), where 1⩽p0) is arbitrary; the nonlinear term f is supposed to satisfy the growth condition |f′(s)|⩽C4(1+|s|q), where q⩽2. It is remarkable that when 2