Weighted Stepanov-Like Pseudo Almost Automorphic Solutions for Evolution Equations and Applications

Abstract

In this paper, the existence and stability of (weighted) Stepanov-like pseudo almost automorphic solutions are proved for a large class of linear and semilinear evolution equations in interpolation spaces. Our method is based on the one hand on a combination of differential inequalities and interpolations functors for the case of linearized equation, and on the other hand on the fixed point argument for the semi-linear equations to handle the case of (weighted) Stepanov-like pseudo almost automorphic functions. Finally, we apply the abstract results to various problems of incompressible viscous fluid flows.