(untitled) (ҚазҰУ Хабаршысы. Математика, механика, информатика сериясы, 2022)
This article discusses the problems of studying the issue of joint motion of liquids in the porous space. The article provides the construction of a mathematical model of the theory of ltration, which describes phase transitions. The main diculty in constructing this model is associated with the fact that free interphase boundaries create regions that change over time, and it is required to nd the temperature or concentration elds of substances in them. In this case, the coordinates of the considered phase boundaries are not initially specied and must be calculated already in the process of solving. For this, a derivation of the averaged equation for the problem of nding the rupture surface during the movement of two incompressible viscous liquids in the pores of the soil skeleton was proposed. The article deals with the case when the skeleton is an absolutely rigid body. The rationale was given for the choice of an averaged ltration model instead of a microscopic one. The main research methods are classical methods of mathematical physics, functional analysis and computation methods of the theory of partial dierential equations, as well as dierence methods. The formulation of the problem is given, and the denition of a generalized solution for solving the problem is provided. Next, an averaged model is derived and the existence of at least one generalized solution to the problem is proved.