Asymptotic Smoothing and Global Attractors for a Class of Nonlinear Evolution Equations. (21st May 2013)

• Record Type: Journal Article
• Authors: Xie, Yongqin; He, Zhufang; Xi, Chen; Jun, Zheng
• Other Names: Liu S. Academic Editor.; Shen W. Academic Editor.
• Is Part Of: ISRN mathematical analysis. Volume 2013(2013)
• Publication Date: 2013-05-21
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Periodicals; 515
• DOI: 10.1155/2013/989475
• Languages: English
• ISSNs: 2090-4657

Abstract

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.