Global attractors for semilinear damped wave equations with critical exponent on Rn

Long-time dynamical properties for a class of semilinear damped wave equations with critical exponent on unbounded domain Rn are studied. The existence of compact global attractors for these equations in natural energy space is proved. These attractors are characterized as the unstable manifold of the set of stationary points, due to the existence of a Lyapunov functional.