## Differential and Integral Equations

### Robustness of asymptotic properties of evolution families under perturbations

Lahcen Maniar

#### Abstract

In this paper, we present some conditions under which asymptotic properties of an evolution family ${{\mathcal{U}}}:={(U(t,s))_{t\geq s\geq 0}}$ persist under perturbations by a family $\mathcal B:=(B(t),D(B(t))_{t\in{{\mathbb{R_+}}}}$ of linear operators on a Banach space $X$ satisfying suitable conditions. Our results concern asymptotic properties like boundedness, periodicity, and asymptotic almost periodicity (even in the sense of Eberlein). An application of the abstract results to nonautonomous partial differential equations with delay is given.

#### Article information

Source
Differential Integral Equations Volume 17, Number 11-12 (2004), 1309-1319.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060248

Mathematical Reviews number (MathSciNet)
MR2100029

Zentralblatt MATH identifier
1150.47322

#### Citation

Maniar, Lahcen. Robustness of asymptotic properties of evolution families under perturbations. Differential Integral Equations 17 (2004), no. 11-12, 1309--1319.https://projecteuclid.org/euclid.die/1356060248