Geodesic
Non-equilibrium two phase filtration
Matematičeskoe modelirovanie, Tome 18 (2006) no. 10, pp. 19-38

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In this paper we analyze a boundary-value problem of a Goursat type for non-equilibrium two-phase filtrations equations. We demonstrate consistency of initial and boundary conditions in the sense of existence of a continuous solution. In a special case for Backley–Leveret linear function we obtain the faithful solution depending on boundary conditions. 
@article{MM_2006_18_10_a2,
     author = {G. T. Bulgakova and T. A. Faizullin and A. V. Zhiber},
     title = {Non-equilibrium two phase filtration},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {19--38},
     publisher = {mathdoc},
     volume = {18},
     number = {10},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2006_18_10_a2/}
}
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G. T. Bulgakova; T. A. Faizullin; A. V. Zhiber. Non-equilibrium two phase filtration. Matematičeskoe modelirovanie, Tome 18 (2006) no. 10, pp. 19-38. http://geodesic.mathdoc.fr/item/MM_2006_18_10_a2/