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Mathematica Slovaca

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Volume 65, Issue 1

Issues

Existence Results for Some Higher-Order Evolution Equations with Time-Dependent Unbounded Operator Coefficients

Toka Diagana
Published Online: 2015-03-25 | DOI: https://doi.org/10.1515/ms-2015-0011

Abstract

In this paper we establish the existence of C(n)-pseudo almost automorphic mild solutions to some n-order evolution equations involving not only time-dependent operator coefficients but also pseudo almost automorphic forcing terms. To illustrate our abstract results, the existence of C(2)-pseudo almost automorphic mild solutions to some damped second-order nonautonomous differential equations, which among other things model the nonautonomous damped beam equation, will be discussed.

Keywords: evolution family; higher-order evolution equations; exponential dichotomy; exponentially stable; Acquistapace-Terreni; damped second-order differential equation; bean equation; C(n)-pseudo-almost automorphic

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About the article

Received: 2012-06-02

Accepted: 2012-09-09

Published Online: 2015-03-25

Published in Print: 2015-02-01


Citation Information: Mathematica Slovaca, Volume 65, Issue 1, Pages 121–140, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.1515/ms-2015-0011.

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