Open Access
2004 Robustness of asymptotic properties of evolution families under perturbations
Lahcen Maniar
Differential Integral Equations 17(11-12): 1309-1319 (2004). DOI: 10.57262/die/1356060248


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.


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Lahcen Maniar. "Robustness of asymptotic properties of evolution families under perturbations." Differential Integral Equations 17 (11-12) 1309 - 1319, 2004.


Published: 2004
First available in Project Euclid: 21 December 2012

zbMATH: 1150.47322
MathSciNet: MR2100029
Digital Object Identifier: 10.57262/die/1356060248

Primary: 47D06
Secondary: 34D05 , 34G10 , 47A55 , 47N20

Rights: Copyright © 2004 Khayyam Publishing, Inc.

Vol.17 • No. 11-12 • 2004
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