Asymptotic stability for a viscoelastic equation with the time-varying delay

Abstract

The goal of the present paper is to study the viscoelastic wave equation with the time-varying delay under initial-boundary value conditions. By using the multiplier method together with some properties of the convex functions, the explicit and general stability results of the total energy are proved under the general assumption on the relaxation function g.

Keywords

• viscoelasticity
• delay term
• source term
• energy decay