Geodesic
Boundary value problems for systems of equations of two-phase porous flow type; statement of the problems, questions of solvability, justification of approximate methods
Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 62-80

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A system of two second order quasilinear equations (one elliptic and one parabolic) is investigated. Such a system is formed by the equations of two-phase porous flow. Boundary value problems are considered for the system, and existence, uniqueness, and stability theorems are proved for the solutions of the problems in the nondegenerate plane case. A justification is given for some approximate methods of constructing the solutions. Bibliography: 10 titles. 
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     author = {S. N. Kruzhkov and S. M. Sukoryanskii},
     title = {Boundary value problems for systems of equations of two-phase porous flow type; statement of the problems, questions of solvability, justification of approximate methods},
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S. N. Kruzhkov; S. M. Sukoryanskii. Boundary value problems for systems of equations of two-phase porous flow type; statement of the problems, questions of solvability, justification of approximate methods. Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 62-80. http://geodesic.mathdoc.fr/item/SM_1977_33_1_a4/