Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 60, pp. 1-9.

Title: Almost automorphy of semilinear parabolic evolution equations
 
Authors: Mahmoud  Baroun (Univ. Cadi Ayyad, Morocco)
         Said Boulite    (Univ. Cadi Ayyad, Morocco)
	 Gaston M. N'Guerekata (Morgan State Univ., Baltimore, MD, USA)
	 Lahcen Maniar   (Univ. Cadi Ayyad, Morocco)

Abstract: 
 This paper studies the existence and uniqueness of  almost
 automorphic mild  solutions to the semilinear  parabolic
 evolution equation
 $$
 u'(t)=A(t)u(t)+f(t, u(t)),
 $$
 assuming that the linear  operators $A(\cdot)$ satisfy the
 Acquistapace-Terreni conditions,  the evolution family
 generated by $A(\cdot)$ has an exponential dichotomy, and
 the resolvent $R(\omega,A(\cdot))$, and $f$ are almost automorphic.
 
Submitted December 19, 2007. Published April 22, 2008.
Math Subject Classifications: 34G10, 47D06.
Key Words: Parabolic evolution equations; almost automorphy;
           exponential dichotomy; Green's function.