  In this paper, we study the Cauchy problem for a nonlinear wave equation with
frictional and viscoelastic damping terms. As is pointed out by [8], in this
combination, the frictional damping term is dominant for the viscoelastic one
for the global dynamics of the linear equation. In this note we observe that if
the initial data is small, the frictional damping term is again dominant even
in the nonlinear equation case. In other words, our main result is diffusion
phenomena: the solution is approximated by the heat kernel with a suitable
constant. Our proof is based on several estimates for the corresponding linear
equations.
