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

Abstract

In this paper, a class of non-linear Integro-differential equations is considered in a bounded domain Ω with a smooth boundary ∂Ω as follows: utt + M(kD muk 2 2)(−∆)mu(t) + Z t 0 g(t − s)(−∆)mu(s)ds + |ut| α−1 ut = |u| p−1 u. The asymptotic behavior of solutions is discussed by some conditions on g. Decay estimates of the energy function of solutions are also given.