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2002 The asymptotic behaviour of perturbed evolution families
Valentina Casarino, Lahcen Maniar, Susanna Piazzera
Differential Integral Equations 15(5): 567-586 (2002).

Abstract

Given an evolution family $\mathcal U:={(U(t,s))_{t\geq s}}$ on a Banach space $X$, we present some conditions under which asymptotic properties of $\mathcal U$ are stable under small perturbations by a family $$ \mathcal{B}:=(B(t),D(B(t))_{t\in\mathbb{J}},$$ $\mathbb{J} =\mathbb{R}$ or $\mathbb{R}_+$, of linear closed operators on $X$. Our results concern asymptotic properties like periodicity, (asymptotic) almost periodicity (even in the sense of Eberlein), uniform ergodicity and total uniform ergodicity. We present, moreover, an application of the abstract results to non-autonomous partial differential equations with delay.

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Valentina Casarino. Lahcen Maniar. Susanna Piazzera. "The asymptotic behaviour of perturbed evolution families." Differential Integral Equations 15 (5) 567 - 586, 2002.

Information

Published: 2002
First available in Project Euclid: 21 December 2012

zbMATH: 1042.47031
MathSciNet: MR1895896

Subjects:
Primary: 47D06
Secondary: 34D05 , 34D10 , 34G10

Rights: Copyright © 2002 Khayyam Publishing, Inc.

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Vol.15 • No. 5 • 2002
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