On a Forced Quasilinear Hyperbolic Volterra Equation with Fading Memory

In this paper we prove the global existence of a solution to a boundary initial value problem for a forced quasilinear hyperbolic Volterra equation under the assump- tion that the forcing term remains small and can be decom- posed into a time-periodic part and a part that decays to zero as t →∞ . We also show that the solution converges to a time- periodic function as t →∞ ; the latter is a periodic solution of a related history value problem.