On the existence of almost automorphic generalized solutions to some generalized differential equations

Abstract

This paper is devoted to study some regularity of almost automorphic and asymptotic almost automorphic generalized solution of the differential equation d dtu(t) = Au(t) + f(t), in the framework of the Colombeau algebras. Under certain assumptions about the second member we showed that the generalized solution is an asmptotically almost automorphic in the sense of genaralized functions.