ALMOST AUTOMORPHIC SOLUTIONS FOR NONAUTONOMOUS PARABOLIC EVOLUTION EQUATIONS

Mahmoud Baroun , Khalil Ezzinbi (1) , Kamal Khalil , Lahcen Maniar (2)

1 [MRC-CAD] - Department of Mathematics [Marrakech]
2 UCA - Université Cadi Ayyad [Marrakech]

In this work, we study the existence and uniqueness of an almost automorphic solution to semilinear nonautonomous parabolic evolution equations with inhomogeneous boundary conditions using the exponential dichotomy. We assume that the homogeneous problem satisfies the "Acquistapace-Terreni" conditions and that the forcing terms are Stepanov-like almost automorphic. An example is given for illustration .

Mots clés: Parabolic evolution equations; Stepanov almost automorphic functions; Evolution family; Extrapolation and interpolation spaces; exponential dichotomy; µ-pseudo almost automorphic functions

Domaines: Equations aux dérivées partielles [math.AP]

Mahmoud Baroun, Khalil Ezzinbi, Kamal Khalil, Lahcen Maniar. ALMOST AUTOMORPHIC SOLUTIONS FOR NONAUTONOMOUS PARABOLIC EVOLUTION EQUATIONS. Semigroup Forum, In press. ⟨hal-02019534⟩