Pseudo almost periodic solutions for some parabolic evolution equations with Stepanov-like pseudo almost periodic forcing terms

The aim of this work is to study the existence and uniqueness of μ-pseudo almost periodic solutions to a class of semilinear parabolic evolution equations with inhomogeneous boundary conditions, under the assumption that the forcing terms of the equation are μ-pseudo almost periodic in the sense of Stepanov. We also provide a new composition result of μ-pseudo almost periodic functions in the sense of Stepanov. An example is given for illustration.