Boundary stabilization for the stretched string equation

We consider a quasilinear partial integro-differential equation modelling the vibrations of a nonlinear string.In the presence of an appropriate boundary damping, we prove a global existence and uniqueness result, for "small" initial data.By the use of suitably chosen Lyapunov functionals, we also show the exponential decay of the energy for any strong solution and we give precise estimates of the rate of decay.