Travelling waves of phase transitions in porous media

Liquid-vapour phase changes for a fluid flow through a porous medium are considered; in particular, the model allows for phase mixtures and includes an equilibrium pressure. Existence and uniqueness of travelling waves is established in a wide range of situations; the end states may be formed either by pure phases or mixtures; in the latter case the pressure equals the equilibrium pressure. A formal asymptotic analysis for vanishing relaxation time is carried out to show that the friction and reaction source terms have smoothing effect when the pressure is close to the equilibrium pressure and pure phases are avoided.