Stability of viscoelastic wave equation with distributed delay and logarithmic nonlinearity

Abstract

In this paper, we consider a quasilinear viscoelastic wave equation that features a distributed delay as well as logarithmic nonlinearity. We combine the potential well theory, Faedo‐Galerkin's approximation, and some energy estimates to construct the global existence of the solution. With weaker conditions on the relaxation function, we establish explicit and general decay rate results by using the multiplier method and some properties of convex functions. Our results improve and generalize several earlier related results in the literature.