(untitled) (ҚазҰУ Хабаршысы. Математика, механика, информатика сериясы, 2023)
The processes of immiscible liquids in porous media are one of the current topics in the modern world, where advanced technologies are used to obtain the most comprehensive information about the geological and geophysical properties of reservoirs. The process of separating two immiscible liquids at a contact surface without surface tension describes the phenomenon when two different types of liquids are in direct contact with each other without the formation of an interface boundary or surface tension between them. This phenomenon can be observed when certain conditions are met, and it is important in various scientific and engineering fields. It is well-known that all hydrodynamic processes are described by mathematical tools and models, and solving such problems allows for obtaining numerical solutions for practical applications in the future. The authors of the article present the problem statement of two immiscible liquids separated by a contact surface without surface tension. For the adequacy of this problem, the presence and singularity of a classical solution have been proven, which depend on the location of the unfixed boundary. The solution demonstrates the existence of a continuous boundary that divides the region into sections containing by two different liquids, where the initial density distribution is a smooth function.