Geodesic
Almost automorphy of semilinear parabolic evolution equations
Electronic journal of differential equations, Tome 2008 (2008)
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 
@article{EJDE_2008__2008__a70,
     author = {Baroun,  Mahmoud and Boulite,  Said and N'guerekata,  Gaston M. and Maniar,  Lahcen},
     title = {Almost automorphy of semilinear parabolic evolution equations},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1170.34344},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a70/}
}
TY  - JOUR
AU  - Baroun,  Mahmoud
AU  - Boulite,  Said
AU  - N'guerekata,  Gaston M.
AU  - Maniar,  Lahcen
TI  - Almost automorphy of semilinear parabolic evolution equations
JO  - Electronic journal of differential equations
PY  - 2008
VL  - 2008
UR  - http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a70/
LA  - en
ID  - EJDE_2008__2008__a70
ER  - 
%0 Journal Article
%A Baroun,  Mahmoud
%A Boulite,  Said
%A N'guerekata,  Gaston M.
%A Maniar,  Lahcen
%T Almost automorphy of semilinear parabolic evolution equations
%J Electronic journal of differential equations
%D 2008
%V 2008
%U http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a70/
%G en
%F EJDE_2008__2008__a70
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/