Existence of exponential attractors for the plate equations with strong damping

Abstract

We show the existence of $(H_0^2(Omega)imes L^2(Omega), H_0^2(Omega)imes H_0^2(Omega))$-global attractors for plate equations with critical nonlinearity when $gin H^{-2}(Omega)$. Furthermore we prove that for each fixed $T > 0$, there is an ($H_0^2(Omega)imes L^2(Omega), H_0^2(Omega)imes H_0^2(Omega))_{T}$-exponential attractor for all $gin L^2(Omega)$, which attracts any $H_0^2(Omega)imes L^2(Omega)$-bounded set under the stronger $H^2(Omega)imes H^2(Omega)$-norm for all $tgeq T$.

Keywords

• Plate equation
• critical exponent
• exponential attractor