Decay property of solutions to the wave equation with space-dependent
damping, absorbing nonlinearity, and polynomially decaying data
Abstract
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.