Analytical Solution of the Cauchy Problem for a Nonstationary Three-dimensional Model of the Filtration Theory

Authors

  • Aigerim T. Rakhymova L.N.Gumilyov Eurasian National University, 010000 Nur Sultan, Kazakhstan
  • Mars B. Gabbassov "Factor" System Research Company LLP, L.N.Gumilyov Eurasian National University, 010000 Nur Sultan, Kazakhstan
  • Anvarjon A. Ahmedov Pusat Sains Matematik, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Kuantan, Pahang, Malaysia

DOI:

https://doi.org/10.37934/arfmts.87.1.118133

Keywords:

four dimensional space, regular function, filtration, nonlinear equation, Cauchy problem

Abstract

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.

Author Biographies

Aigerim T. Rakhymova, L.N.Gumilyov Eurasian National University, 010000 Nur Sultan, Kazakhstan

aigerim_rakhimova@mail.ru

Mars B. Gabbassov, "Factor" System Research Company LLP, L.N.Gumilyov Eurasian National University, 010000 Nur Sultan, Kazakhstan

gmarson19@gmail.com

Anvarjon A. Ahmedov, Pusat Sains Matematik, Universiti Malaysia Pahang, Lebuhraya Tun Razak, 26300 Gambang, Kuantan, Pahang, Malaysia

anvarjon@ump.edu.my

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Published

2021-09-10

How to Cite

Rakhymova, A. T. ., Gabbassov, M. B., & Ahmedov, A. A. . (2021). Analytical Solution of the Cauchy Problem for a Nonstationary Three-dimensional Model of the Filtration Theory. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 87(1), 118–133. https://doi.org/10.37934/arfmts.87.1.118133

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