Exponential decay and global existence of solutions of a singular nonlocal viscoelastic system with distributed delay and damping terms


Abdelbaki Choucha, Salah Boulaaras, Djamel Ouchenane




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])