Asymptotic behavior of solutions to a nonautonomous semilinear evolution equation

Xiao-Xia Luo; Yong-Long Wang

doi:10.26637/mjm203/014

Abstract

In this paper, we shall deal with \(\mu\)-pseudo almost automorphic solutions to the nonautonomous semilinear evolution equations: \(u^{\prime}(t)=A(t) u(t)+f(t, u(t-h)), t \in \mathbb{R}\) in a Banach space \(\mathbb{X}\), where \(A(t), t \in \mathbb{R}\) generates an exponentially stable evolution family \(\{U(t, s)\}\) and \(f: \mathbb{R} \times \mathbb{X} \rightarrow \mathbb{X}\) is a \(\mu\)-pseudo almost automorphic function satisfying some suitable conditions. We obtain our main results by properties of \(\mu\)-pseudo almost automorphic functions combined with theories of exponentially stable evolution family.

Keywords:

nonautonomous semilinear evolution equations, fixed point, \(\mu\)-pseudo almost automorphic function

Mathematics Subject Classification:

34K14, 60H10, 35B15, 34F05

Authors Imprint References Funding Related Articles Downloads

Xiao-Xia Luo Department of Mathematics, Lanzhou Jiaotong University,Lanzhou - 730070, P. R. China.
Yong-Long Wang Department of Mathematics, Lanzhou Jiaotong University,Lanzhou - 730070, P. R. China.

Pages: 277-286
Date Published: 01-07-2014
Vol. 2 No. 03 (2014): Malaya Journal of Matematik (MJM)

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