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.