Energy decay for wave equations with nonlinear damping and space-time coefficient in Rn

In this paper, we consider the following nonlinear wave equation {u(tt) - ?u +/- a(t,x)|u(t)|(m-1)u(t) + |u|(p-1)u = 0, t > 0, x is an element of R(n)u(0,x) = u(0)(x), u(t)(0,x) = u(1)(x) x is an element of R-n and obtain optimal energy decay estimates under suitable assumptions on the space-time nonlinear damping coefficient a, where m satisfies 1 < m ? n+2/n-2 . We establish a new Liapunov type function to obtain energy decay estimates in the case of nonlinear damping instead of the Kormonik lemma.