. For the system of equations of two-component, two-phase filtration, which in fact is not parabolic neither hyperbolic, the solution of the Riemann problem is described. The Riemann problem is thought of as the Cauchy problem with constant initial function for positive and negative values of space coordinate. The Hugoniot relations are obtained and stability conditions are proposed in the framework of P.Lax stability conditions. For this setting some qualitative properties of Riemann problem solutions are inferred that confirm the intermediate character of the system under consideration. Also the process of solutions construction is described and the arguments about the validity of existence and uniqueness theorems are shown. The rigorous proofs are not given in the present study.

Mathematical problems and theory of numerical methods