Decay For The Solution Of Three Nonlinear Evoluation Equations

In this paper we obtain an exponential rate of decay for the solution of equations by constructing a suitable Lyapunov function: And a local energy result is derived to the following nonlinear wave equation using the technique of Matsuyama[19]and Todorova-Yordanov[20]: utt-div(k(x)(?)u)+u|u|p-2=0. Here the kernel g in the memory term decays exponentially and u is a function about the variable of t,x.