On convexity for energy decay rates of a viscoelastic wave equation with a dynamic boundary and nonlinear delay term

Abstract

In this work, we investigate the initial boundary value problem for a system of viscoelastic wave equations in a bounded domain with dynamic boundary conditions related to the Kelvin Voigt damping and nonlinear delay term acting on the boundary. At first, the global existence of solutions is discussed using the potential well method and introducing suitable energy and Lyapunov functionals to establish general decay estimates.