On decay and blow-up of solutions for a system of viscoelastic equations with weak damping and source terms

In this article, we investigate a system of two viscoelastic equations with Dirichlet boundary conditions. Under some suitable assumptions on the function g(i)(center dot), f(i)(center dot, center dot) (i = 1, 2) and the initial data, we obtain general and optimal decay results. Moreover, for certain initial data, we establish a finite time blow-up result. This work generalizes and improves earlier results in the literature. The conditions of the relaxation functions g(1)(t) and g(2) (t) in our work are weak and seldom appear in previous literature, which is an important breakthrough.