Attractors for a Class of Abstract Evolution Equations with Fading Memory. (14th June 2017)

• Record Type: Journal Article
• Authors: Wang, Xuan; Duan, Fenxia; Hu, Didi
• Other Names: Sadarangani Kishin Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2017(2017)
• Publication Date: 2017-06-14
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2017/1410408
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : In this paper, we study the dynamics of an abstract evolution equation with fading memory with a critical growing nonlinearity. By use of some new methods and asymptotic estimate techniques, we first verify the asymptotic compact of solution semigroup and then prove the existence of global attractors in weak topological space and strong topological space, while the forcing term only belongs to H - 1 ( Ω ) or L 2 ( Ω ), respectively. The results are new and appear to be optimal.