In this paper, a singular one-dimensional viscoelastic system with a nonlinear source term, nonlocal boundary condition and damping terms is considered. We prove the existence of a global solution using the potential-well theory. Furthermore, by constructing Lyapunov functional combined with the perturbed energy method, the general decay result is proved.
"Global existence and decay of solutions of a singular nonlocal viscoelastic system with damping terms." Topol. Methods Nonlinear Anal. 56 (1) 283 - 312, 2020. https://doi.org/10.12775/TMNA.2020.014