Differential and Integral Equations

Robustness of asymptotic properties of evolution families under perturbations

Lahcen Maniar

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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

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

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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

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