Diffusion in porous media with hysteresis and bounded speed of propagation

It is shown that the problem of moisture propagation in porous media with a nonlinear relation between the mass flux and the pressure gradient as a counterpart of the Darcy law exhibits the property of bounded speed of propagation even in the case of a hysteresis relation between the capillary pressure and the moisture content. The paper specifies conditions for existence and uniqueness of solutions, and provides an upper bound for the moisture propagation speed.