  In this paper we consider the local energy decay result for wave equations
with a short-range potential. It is important to note that one never uses a
finite speed of propagation property unlike the historical previous papers. The
essential parts of analysis are in getting L^2-bound of the solution itself,
and deriving the weighted energy estimates. In this paper we only use a simple
multiplier method to treat the variable coefficient case, and do not rely on
any resolvent estimates.

Analysis of PDEs