Global attractor and decay estimates of solutions to a class of nonlinear evolution equations

Abstract

In this work, we prove the existence of global attractor for the nonlinear evolution equation utt−Δu−Δut−Δutt + g(x, u)=f(x) in X=(H2(Ω)∩H(Ω)) × (H2(Ω)∩H(Ω)). This improves a previous result of Xie and Zhong in (J. Math. Anal. Appl. 2007; 336:54–69.) concerning the existence of global attractor in H(Ω) × H(Ω) for a similar equation. Further, the asymptotic behavior and the decay property of global solution are discussed. Copyright © 2010 John Wiley & Sons, Ltd.