Geodesic
Almost automorphy of semilinear parabolic evolution equations
Electronic Journal of Differential Equations, Tome 2008 (2008).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34G10, 47D06
Keywords: parabolic evolution equations, almost automorphy, exponential dichotomy, Green's function 
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     author = {Baroun, Mahmoud and Boulite, Said and N'guerekata, Gaston M. and Maniar, Lahcen},
     title = {Almost automorphy of semilinear parabolic evolution equations},
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     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a70/}
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Baroun, Mahmoud; Boulite, Said; N'guerekata, Gaston M.; Maniar, Lahcen. Almost automorphy of semilinear parabolic evolution equations. Electronic Journal of Differential Equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a70/