  We study the large time behavior of solutions to the wave equation with
space-dependent damping in an exterior domain. We show that if the damping is
effective, then the solution is asymptotically expanded in terms of solutions
of corresponding parabolic equations. The main idea to obtain the asymptotic
expansion is the decomposition of the solution of the damped wave equation into
the solution of the corresponding parabolic problem and the time derivative of
the solution of the damped wave equation with certain inhomogeneous term and
initial data. The estimate of the remainder term is an application of weighted
energy method with suitable supersolutions of the corresponding parabolic
problem.
