µ-Pseudo almost periodic solutions for some hyperbolic evolution equations with Stepanov pseudo almost periodic forcing terms

Thami Akrid; Mahmoud Baroun; Lahcen Maniar; Academic Editor: Youssef EL FOUTAYENI

Research Communication | Open Access
Volume 2019 | Communication ID 317

µ-Pseudo almost periodic solutions for some hyperbolic evolution equations with Stepanov pseudo almost periodic forcing terms

Thami Akrid, Mahmoud Baroun, Lahcen Maniar

Academic Editor: Youssef EL FOUTAYENI

Received	Accepted	Published
Feb 14, 2019	Feb 26, 2019	Mar 01, 2019

Abstract: This work deals with the existence and uniqueness of µ-pseudo almost periodic solutions to some semilinear hyperbolic evolution equations with inhomogeneous boundary conditions of the form (1) The first equation stands in a Banach space X, called state space, and the second one in a Banach space ∂X, called boundary space. We assume that A:= /KerL generates a C_0-semigroup on a Banach space X. Under Greiner’s assumptions (see [4]) on the boundary operator L, and the forcing terms f and g, taking values in X and in ∂X ...