A general decay estimate for the nonlinear transmission problem of weak viscoelastic equations with time-varying delay

Abstract

The transmission of waves over a body composed of two different materials is considered in this paper. One component is a simple elastic part, while the other is a weak viscoelastic component with time-varying delay and damping effect. Besides, one part of the boundary is controlled by a nonlinear memory source term, while the other part is clamped. Under the influence of time-varying delay and damping effect, we derive a general decay estimate of the energy when the memory kernels in the internal weak viscoelasticity and boundary source decay simultaneously.