Geodesic
An initial boundary-value problem for the equations of three-phase immiscible capillary flows in porous media
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 2, pp. 103-113

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A classical model for three phase capillary immiscible flows in a porous medium is considered. Capillarity pressure functions are found, with a corresponding diffusion-capillarity tensor being triangular. The model is reduced to a degenerate quasilinear parabolic system. A global existence theorem is proved under some hypotheses on the model data. 
@article{VNGU_2006_6_2_a7,
     author = {V. V. Shelukhin},
     title = {An initial boundary-value problem for the equations of three-phase immiscible capillary flows in porous media},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {103--113},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2006_6_2_a7/}
}
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V. V. Shelukhin. An initial boundary-value problem for the equations of three-phase immiscible capillary flows in porous media. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 6 (2006) no. 2, pp. 103-113. http://geodesic.mathdoc.fr/item/VNGU_2006_6_2_a7/