Interface conditions for degenerate two-phase flow equations in one space dimension

Abstract

We study the two-phase flow equations describing, e.g., the motion of oil and water in a porous material, and are concerned with interior interfaces where two different porous media are in contact. At such an interface, the entry pressure relation together with the degeneracy of the system leads to an interesting effect known as oil-trapping. Restricting to the one-dimensional case we show an existence result with the help of appropriate regularizations and a time discretization. The crucial tool is a compactness lemma: The control of the time derivative in a space of measures is used to conclude the strong convergence of a sequence.