ABSTRACT:
We show the (asymptotic) almost periodicity of the bounded solution
to the parabolic evolution equation $u'(t)=A(t)u(t)+f(t)$ on $\RR$
(on $\RR_+$) assuming that the linear operators $A(t)$ satisfy the
`Acquistapace--Terreni' conditions, that the evolution family generated by
$A(\cdot)$  has an exponential dichotomy, and that $R(\omega,A(\cdot))$
and $f$ are (asymptotically) almost periodic.



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Roland Schnaubelt                                      Phone: +49-345-5524627
Fachbereich Mathematik und Informatik                    Fax: +49-345-5527003
Martin-Luther-Universitaet Halle-Wittenberg
06099 Halle (Saale),  Germany
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Office Nr.202 at Theodor-Lieser-Str.5,   06120 Halle
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Email: schnaubelt@mathematik.uni-halle.de