Differential and Integral Equations

Robustness of asymptotic properties of evolution families under perturbations

Lahcen Maniar

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Subjects
Primary: 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]
Secondary: 34D05: Asymptotic properties 34G10: Linear equations [See also 47D06, 47D09] 47A55: Perturbation theory [See also 47H14, 58J37, 70H09, 81Q15] 47N20: Applications to differential and integral equations

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.


Export citation