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
assuming that the linear operators
satisfy the
Acquistapace-Terreni conditions, the evolution family
generated by
has an exponential dichotomy, and
the resolvent
, and
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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