# Initial-boundary value problem for the damped wave equation with nonlinear source (in bounded domains)

It is well known that the initial-value problem for the wave equation on $$\mathbb R^N$$ can be studied by means of Fourier transform.

What reference presents well-posedness results and qualitative properties (decay, speed of propagation) of the damped wave equation with nonlinear source on a bounded domain?

What are the differences with respect to the corresponding results in the whole space?