Long-time behaviour of a porous medium model with degenerate hysteresis

Hysteresis in the pressure-saturation relation in unsaturated porous media, owing to surface tension on the liquid–gas interface, exhibits strong degeneracy in the resulting mass balance equation. As an extension of previous existence and uniqueness results, we prove that under physically admissible initial conditions and without mass exchange with the exterior, the unique global solution of the fluid diffusion problem exists and asymptotically converges as time tends to infinity to a possibly non-homogeneous mass distribution and an a priori unknown constant pressure. This article is part of the theme issue ‘Non-smooth variational problems with applications in mechanics’.