Energy Decay of the Solution for a Weak Viscoelastic Equation with a Time-Varying Delay

In this paper, we consider a weak viscoelastic equation with internal time-varying delay u_tt(x, t)- u(x, t)+α(t) ∫_0^tg(t-s) u(x, s)ds+μ u_t(x, t-τ(t))=0 in a bounded domain. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we establish a general decay result for the energy. This work generalizes and improves earlier results in the literature.