Attractors for a Class of Abstract Evolution Equations with Fading Memory

Xuan Wang, Fenxia Duan and Didi Hu

Mathematical Problems in Engineering, 2017, vol. 2017, 1-16

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.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:1410408

DOI: 10.1155/2017/1410408

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