Exponential Decay and Global existence of solutions of a singular nonlocal viscoelastic system with distributed delay and damping terms

Abstract

We investigate in this work a singular one-dimensional viscoelastic system with  a nonlinear source term,  distributed delay, nonlocal boundary condition, and damping terms. By the theory of potential-well, the existence of a global solution is established, and by the energy method and the functional of Lyapunov, we prove the exponential decay result. This work is an extension of Boulaaras' work in  ([3] and [27]).