Exponential decay of non-linear wave equation with a viscoelastic boundarycondition

We study in this paper the global existence and exponential decay of soluti ons of the non-linear unidimensional wave equation With a viscoelastic boun dary condition. We prove that the dissipation induced by the memory effect is strong enough to secure global estimates, which allow us to show existen ce of global smooth solution for small initial data. We also prove that the solution decays exponentially provided the resolvent kernel of the relaxat ion function, k decays exponentially. When k decays polynomially, the solut ion decays polynomially and with the same rate. Copyright (C) 2000 John Wil ey & Sons, Ltd.