Open AccessAnalytical Solution of the Cauchy Problem for a Nonstationary Three-dimensional Model of the Filtration Theory
Author(s) -
A. T. Rakhymova,
M. B. Gabbassov,
Anvarjon Ahmedov
Publication year - 2021
Publication title -
journal of advanced research in fluid mechanics and thermal sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.247
H-Index - 13
ISSN - 2289-7879
DOI - 10.37934/arfmts.87.1.118133
Subject(s) - mathematics , filtration (mathematics) , cauchy problem , mathematical analysis , nonlinear system , cauchy distribution , space (punctuation) , work (physics) , initial value problem , complete metric space , physics , pure mathematics , computer science , quantum mechanics , thermodynamics , operating system , banach space
This paper is devoted to the study of the Cauchy problem for a system of differential equations describing the unsteady flow of a compressible fluid in a homogeneous and inhomogeneous porous medium with a general nonlinear filtration law in three-dimensional space. In the work using the methods of four-dimensional mathematics, a special four-dimensional space of space and time coordinates was developed, as well as a functional space of regular functions, and analytical conditions were obtained on the general form of the nonlinear filtration law for which the Cauchy problem has a solution.