Asymptotic behavior of solutions to a nonautonomous semilinear evolution equation

Xiao-Xia Luoa,* and Yong-LongWangb

Asymptotic behavior of solutions to a nonautonomous semilinear evolution equation

Authors :

Xiao-Xia Luo^a,* and Yong-LongWang^b

Author Address :

^a,bDepartment of Mathematics, Lanzhou Jiaotong University,Lanzhou - 730070, P. R. China.

*Corresponding author.

Abstract :

In this paper, we shall deal with $mu$-pseudo almost automorphic solutions to the nonautonomous semilinear evolution equations: $u’(t)=A(t)u(t)+f(t,u(t-h))$, $tin mathbb{R}$ in a Banach space $mathbb{X}$, where $A(t)$, $tin mathbb{R}$ generates an exponentially stable evolution family ${U(t,s)}$ and $f:mathbb{R} imesmathbb{X} ightarrowmathbb{X}$ 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 :

$mu$-pseudo almost automorphic function, nonautonomous semilinear evolution equations, fixed point.

DOI :

Article Info :

Received : February 13, 2014; Accepted : April 25, 2014.