Exponential attractors for the strongly damped wave equations

For the strongly damped wave equation with critical nonlinearity, we First show the existence of a (H-0(1)(Omega) x L-2(Omega), H-0(1)(Omega) x H-0(1)(Omega))-global attractor when the external forcing g is an element of H-1; then we prove that for each T > 0 fixed, there is abounded (in H-2 x H-1) set which attracts exponentially every H-1 x L-2 -bounded set w.r.t. the stronger H-1 x H-1-norm for all t >= T and has finite fractal dimension in H-0(1)(Omega) x H-0(1)(Omega) for the case g is an element of L-2(Omega). (C) 2009 Elsevier Ltd. All rights reserved.