  In this paper we consider the long time behavior of solutions of the initial
value problem for the damped wave equation of the form \begin{eqnarray*}
u_{tt}-\rho(x)^{-1}\Delta u+u_t+m^2u=f(u) \end{eqnarray*} with some $\rho(x)$
and $f(u)$ on the whole space $\R^n$ ($n\geq 3$).
  For the low initial energy case, which is the non-positive initial energy,
based on concavity argument we prove the blow up result. As for the high
initial energy case, we give out sufficient conditions of the initial datum
such that the corresponding solution blows up in finite time.
