Traveling waves in porous media with phase-dependent damping

We consider a simple model for the fluid flow in a porous medium. The model consists of a hyperbolic system of balance laws, which take into account phase changes and allow for metastable states thanks to the introduction of an equilibrium pressure. A damping term is included as well, which depend not only on the velocity but also on the phase of the fluid; in particular, it vanishes in the vapor phase. The existence and uniqueness of traveling waves is proved in several important cases.