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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 1410408, 16 pages
https://doi.org/10.1155/2017/1410408
Research Article

Attractors for a Class of Abstract Evolution Equations with Fading Memory

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Correspondence should be addressed to Xuan Wang; nc.ude.unwn@nauxgnaw

Received 1 January 2017; Accepted 27 April 2017; Published 14 June 2017

Academic Editor: Kishin Sadarangani

Copyright © 2017 Xuan Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 or , respectively. The results are new and appear to be optimal.