Problem of capillary displacement for one model of three-phase filtration

The class of capillary pressures corresponding to a triangular tensor of capillary diffusion in a three-phase fluid is studied. Filtration with such a tensor is described by a parabolic system of equations degenerating on solutions. This system is integrodifferential because the desired quantities are the total flow rate and the phase-saturation distribution under conditions of a specified pressure drop on the boundaries of the flow region in one of the phases. It is shown that in the problem of capillary displacement, the degenerate system can be studied using a special maximum principle.