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Hysteresis in the pressure-saturation relation in unsaturated porous media,which is due to surface tension on the liquid-gas interface, exhibits strongdegeneracy in the resulting mass balance equation. As an extension of previousexistence and uniqueness results, we prove that under physically admissibleinitial conditions and without mass exchange with the exterior, the uniqueglobal solution of the fluid diffusion problem exists and asymptoticallyconverges as time tends to infinity to a possibly non-homogeneous massdistribution and an a priori unknown constant pressure.

Long time behavior of a porous medium model with degenerate hysteresis