Global existence and new decay results of a viscoelastic wave equation with variable exponent and logarithmic nonlinearities

In this paper, we consider the following viscoelastic problem with variable exponent and logarithmic nonlinearities: (Formula presented) where γ(.) is a function satisfying some conditions. We first prove a global existence result using the well-depth method and then establish explicit and general decay results under a wide class of relaxation functions and some specific conditions on the variable exponent function. Our results extend and generalize many earlier results in the literature.