General Decay of Energy for a Class of Integro-Differential Equation with Nonlinear Damping

In this paper, a class of non-linear Integro-differential equations is considered in a bounded domain with a smooth boundary @ as follows: utt +M(kDmuk22 )(?
)mu(t) + Z t 0 g(t ? s)(?
)mu(s)ds + |ut|?1ut = |u|p?1u. The asymptotic behavior of solutions is discussed by some conditions on g. Decay estimates of the energy function of solutions are also given.