## Abstract and Applied Analysis

### On the Dynamics of Abstract Retarded Evolution Equations

#### Abstract

This paper is concerned with the dynamics of the following abstract retarded evolution equation: $(d/dt)$ $u(t)+Au(t)=F(u(t-{r}_{1}),\dots ,u(t-{r}_{n}))+g(t)$ in a Hilbert space $H$, where $A:D(A)\subset H\to H$ is a self-adjoint positive-definite operator with compact resolvent and $F:D{({A}^{\alpha })}^{n}\to H$ $(\alpha \in [0,1/2])$ is a locally Lipschitz continuous mapping. The dissipativity and pullback attractors are investigated, and the existence of locally almost periodic solutions is established.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 359310, 9 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393449379

Digital Object Identifier
doi:10.1155/2013/359310

Mathematical Reviews number (MathSciNet)
MR3124034

Zentralblatt MATH identifier
1293.35157

#### Citation

Li, Desheng; Wei, Jinying; Wang, Jintao. On the Dynamics of Abstract Retarded Evolution Equations. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 359310, 9 pages. doi:10.1155/2013/359310. https://projecteuclid.org/euclid.aaa/1393449379

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