Global existence and decay of solutions of a singular nonlocal viscoelastic system with a nonlinear source term, nonlocal boundary condition, and localized damping term

Abstract

The paper deals with the existence of a global solution of a singular one‐dimensional viscoelastic system with a nonlinear source term, nonlocal boundary condition, and localized frictional damping a(x)ut using the potential well theory. Furthermore, the general decay result is proved. We construct a suitable Lyapunov functional and make use of the perturbed energy method.