Uniform energy decay rates for nonlinear viscoelastic wave equation with nonlocal boundary damping

In this paper, we consider the uniform decay estimates of solutions for the viscoelastic wave equation utt−κ0Δu+∫0tg(t−s)div[a(x)∇u(s)]ds+b(x)h(ut)=0in Ω×(0,∞). Under weak assumptions on the functions g,hg,h and ff, we prove the energy functional decays exponentially or polynomially to zero as the time goes to infinity by introducing brief Lyapunov functions and precise priori estimates.