Analytical solution of the cauchy problem for a nonstationary three-dimensional model of the filtration theory

• Main Authors: Rakhymova, Aigerim T., Gabbassov, Mars B., Ahmedov, Anvarjon A.
• Format: Article
• Language: English
• Published: Akademi Baru 2021
• Subjects: QA Mathematics
• Online Access: http://umpir.ump.edu.my/id/eprint/32668/1/Analytical%20solution%20of%20the%20cauchy%20problem%20for%20a%20nonstationary.pdf; http://umpir.ump.edu.my/id/eprint/32668/; https://doi.org/10.37934/arfmts.87.1.118133; https://doi.org/10.37934/arfmts.87.1.118133

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.