Electron. J. Diff. Eqns., Vol. 2008(2008), No. 60, pp. 1-9.

Almost automorphy of semilinear parabolic evolution equations

Mahmoud Baroun, Said Boulite, Gaston M. N'Guerekata, Lahcen Maniar

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.

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Mahmoud Baroun
Department of Mathematics, University Cadi Ayyad
Faculty of Sciences Semlalia
B.P. 2390, 40000 Marrakesh, Morocco
email: m.baroun@ucam.ac.ma
Said Boulite
Department of Mathematics, University Cadi Ayyad
Faculty of Sciences Semlalia
B.P. 2390, 40000 Marrakesh, Morocco
email: sboulite@ucam.ac.ma
Gaston M. N'Guérékata
Department of Mathematics
Morgan State University
Baltimore, MD 21251, USA
email: Gaston.N'Guerekata@morgan.edu
Lahcen Maniar
Department of Mathematics, University Cadi Ayyad
Faculty of Sciences Semlalia
B.P. 2390, 40000 Marrakesh, Morocco
email: maniar@ucam.ac.ma

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