Degenerate diffusion in porous media with hysteresis-dependent permeability

Hysteresis in the relation between the capillary pressure and the moisture content in unsaturated porous media, which is due to surface tension at the liquid-gas interface, exhibits strong degeneracy in the resulting mass balance equation. Solutions to such degenerate equations have been recently constructed by the method of convexification. We show here that the convexification argument works even if the permeability coefficient depends on the hysteretic saturation. The problem of uniqueness remains open in this case.