Exponential attractors for the strongly damped wave equations

摘要

For the strongly damped wave equation with critical nonlinearity, we first show the existence of aa(H01(Ω)XL2(Ω),H01(Ω)XH01(Ω))-global attractor when the external forcing g∈H-1; then we prove that for each T > 0 fixed, there is a bounded (in H2H1) set which attracts exponentially every H1 L2-bounded set w.r.t. the stronger H1 H1-norm for all t≥T and has finite fractal dimension in H10(Ω)　XH01(Ω) for the case g∈L2(Ω).