  We study the large time behavior of solutions to the semilinear wave equation
with space-dependent damping and absorbing nonlinearity in the whole space or
exterior domains. Our result shows how the amplitude of the damping
coefficient, the power of the nonlinearity, and the decay rate of the initial
data at the spatial infinity determine the decay rates of the energy and the
$L^2$-norm of the solution. In Appendix, we also give a survey of basic results
on the local and global existence of solutions and the properties of weight
functions used in the energy method.
