General decay for a viscoelastic wave equation with dynamic boundary conditions and a time-varying delay

TL;DR

This paper investigates the energy decay behavior of a nonlinear viscoelastic wave equation with damping, delay, and dynamic boundary conditions, establishing a general decay result that encompasses exponential and polynomial rates.

Contribution

It introduces a unified approach using energy and Lyapunov functionals to prove a general decay result for the wave equation with complex features, extending previous specific decay rate results.

Findings

Established a general decay theorem for the energy of the system

Unified exponential and polynomial decay as special cases

Provided conditions under which energy decay occurs

Abstract

The goal of this paper is to study a nonlinear viscoelastic wave equation with strong damping, time-varying delay and dynamical boundary condition. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we then prove a general decay result of the energy, from which the usual exponential and polynomial decay rates are only special cases.