In this paper, we are concerned with the energy decay rates for the viscoelastic wave equation with nonlinear damping and nonlinear time-varying delay in the boundary and acoustic boundary conditions. Here we consider with minimal condition on the relaxation function g, namely g ′ ( t ) ≤ − µ ( t ) G ( g ( t ) ) , where G is an increasing and convex function near the origin and µ is a positive nonincreasing function. The decay rates of the energy depend on the functions µ,G and on the function F defined by f 0 which represents the growth at the origin of

In this paper, we consider the general energy decay for weak viscoelastic equation of Kirchhoff type containing Balakrishnan-Taylor damping with nonlinear delay and acoustic boundary conditions. By introducing suitable energy and Lyapunov functionals, we establish the general decay estimates for the energy, which depends on the behavior of both sigma and g.