Evolution equations in generalized Stepanov-like pseudo almost automorphic spaces - Toka Diagana (Electronic Journal of Differential Equations, 2012)
In this article, first we introduce and study the concept of $mathbbS_{gamma}^p$-pseudo almost automorphy (or generalized Stepanov-like pseudo almost automorphy), which is more general than the notion of Stepanov-like pseudo almost automorphy due to Diagana. We next study the existence of solutions to some classes of nonautonomous differential equations of Sobolev type in $mathbbS_{gamma}^p$-pseudo almost automorphic spaces. To illustrate our abstract result, we will study the existence and uniqueness of a pseudo almost automorphic solution to the heat equation with a negative time-dependent diffusion coefficient.