Initial boundary value problem for a viscoelastic wave equation with Balakrishnan-Taylor damping and a delay term: decay estimates and blow-up result

In this paper, we study the initial boundary value problem for the following viscoelastic wave equation with Balakrishnan-Taylor damping and a delay term where the relaxation function satisfies g'(t) <= -xi(t)g(r)(t), t >= 0, 1 <= r < 3/2. The main goal of this work is to study the global existence, general decay, and blow-up result. The global existence has been obtained by potential-well theory, the decay of solutions of energy has been established by introducing suitable energy and Lyapunov functionals, and a blow-up result has been obtained with negative initial energy.