Problem without Initial Conditions for Refined Filtering Model
The article considers the phenomenological equations of fluid motion proposed by V.S. Golubev. The purpose of the research is to propose a fluid motion model that describes this processmore accurately. The objectives of the research are to investigate phenomenological equations, to consider a model with non-averaged density occurrence and a problem without initial conditions for this model. To solve this problem, the methods of the theory of strongly continuous operator semigroups and the correct solvability by S.G. Kerin are used. The findings are as follows: the exact solution for the problem without initial conditions for the proposed filtering model was obtained, which allows us to construct algorithms for computers that simulate the process of fluid motion in a porous medium with stagnant zones with less error. Representations of fluid pressure in the stagnant and flow zones are obtained.