General decay of a viscoelastic wave equation with frictional damping and logarithmic nonlinearity

Abstract

This article is concerned with the energy decay of a viscoelastic wave equation with nonlinear damping and logarithmic nonlinearity, where the memory term involves a matrix-valued coefficient. We successfully establish polynomial decay rates for the solutions to this initial-value problem under relatively weak conditions regarding memory effects. More specifically, we examine both exponential and polynomial decay rates for the solutions under certain assumptions on the kernel of the memory term. Our findings enhance and generalize several earlier related results in the literature.