Asymptotic Smoothing and Global Attractors for a Class of Nonlinear Evolution Equations. (21st May 2013) - Xie, Yongqin; He, Zhufang; Xi, Chen; Jun, Zheng
Abstract : We prove the asymptotic regularity of global solutions for a class of semilinear evolution equations in H 0 1 ( Ω ) × H 0 1 ( Ω ) . Moreover, we study the long-time behavior of the solutions. It is proved that, under the natural assumptions, these equations possess the compact attractor 𝒜 which is bounded in H 2 ( Ω ) × H 2 ( Ω ), where the nonlinear term f satisfies a critical exponential growth condition.