Entropy conditions for heterogeneity induced shocks in two-phase flow problems

We study two-phase flow in a porous medium with piecewise smooth permeability. If capillary forces can not be neglected, the flow problem is parabolic. Without capillary forces this problem degenerates to a hyperbolic conservation law with a discontinuous flux function. The solution for this problem has stationary shocks at discontinuities in the permeability. In this paper we derive an entropy condition for these shocks by studying the limit case of vanishing capillarity.