Poorkarimi and Wiener established the existence of almost periodic solutions to a class of nonlinear hyperbolic partial differential equations with delay. Al-Islam then generalized the results of Poorkarimi and Weiner to the pseudo-almost periodic setting. In this paper, the results of Al-Islam will be extended to the space of weighted pseudo almost periodic functions, also known as Diagana Space. The class of nonlinear hyperbolic partial differential equations of Poorkarimi and Wiener represents a mathematical model for the dynamics of gas absorption.