Boundary value problems for systems of equations of two-phase porous flow type; statement of the problems, questions of solvability, justification of approximate methods

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.