ONE CLASS OF SMOOTH BOUNDED SOLUTIONS TO THE CAUCHY PROBLEM FOR A THREE-DIMENSIONAL FILTRATION MODEL WITH DARCY'S LAW
In the filtration theory there are numerous approaches to solving three-dimensional problems of fluid motion in a porous medium. Basically, the solutions of such problems are obtained by numerical methods. The question of finding an analytical solution of precisely three-dimensional problems of flui...
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| Format: | Article |
| Language: | English |
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Al-Farabi Kazakh National University
2022-06-01
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| Series: | Вестник КазНУ. Серия математика, механика, информатика |
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| Online Access: | https://bm.kaznu.kz/index.php/kaznu/article/view/1083/667 |
| _version_ | 1797937095782694912 |
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| author | A. T. Rakhymova |
| author_facet | A. T. Rakhymova |
| author_sort | A. T. Rakhymova |
| collection | DOAJ |
| description | In the filtration theory there are numerous approaches to solving three-dimensional problems of fluid motion in a porous medium. Basically, the solutions of such problems are obtained by numerical methods. The question of finding an analytical solution of precisely three-dimensional problems of fluid motion is open.
The first results on the use of the apparatus of four-dimensional mathematics for solving the three-dimensional model of the Navier-Stokes equations by the analytical method were obtained by the Kazakh mathematician Professor M.M. Abenov. After the author of this article with other researchers proved the theorem on the existence of a solution to the Cauchy problem for a three-dimensional model of filtration theory.
This paper is devoted to the study of a three-dimensional model of the filtration theory in one of the spaces of four-dimensional numbers. The purpose of this article is to obtain an analytical solution of the three-dimensional Cauchy problem for the mathematical model of linear filtration model by the method of four-dimensional regular functions.
In this study, a class of infinitely differentiable and bounded functions of the initial conditions of the Cauchy problem, satisfying the Cauchy-Riemann condition, with five degrees of freedom for a specific four-dimensional function is found, and also a class of infinitely differentiable and bounded solutions of this problem is found that satisfy the linear Darcy law. |
| first_indexed | 2024-04-10T18:40:32Z |
| format | Article |
| id | doaj.art-4860e61afe86458b961af88f0beb1e1b |
| institution | Directory Open Access Journal |
| issn | 1563-0277 2617-4871 |
| language | English |
| last_indexed | 2024-04-10T18:40:32Z |
| publishDate | 2022-06-01 |
| publisher | Al-Farabi Kazakh National University |
| record_format | Article |
| series | Вестник КазНУ. Серия математика, механика, информатика |
| spelling | doaj.art-4860e61afe86458b961af88f0beb1e1b2023-02-01T14:56:16ZengAl-Farabi Kazakh National UniversityВестник КазНУ. Серия математика, механика, информатика1563-02772617-48712022-06-011142129141https://doi.org/10.26577/JMMCS.2022.v114.i2.013ONE CLASS OF SMOOTH BOUNDED SOLUTIONS TO THE CAUCHY PROBLEM FOR A THREE-DIMENSIONAL FILTRATION MODEL WITH DARCY'S LAWA. T. Rakhymova0https://orcid.org/0000-0002-8888-8686L.N. Gumilyov Eurasian National University, Kazakhstan, Nur-SultanIn the filtration theory there are numerous approaches to solving three-dimensional problems of fluid motion in a porous medium. Basically, the solutions of such problems are obtained by numerical methods. The question of finding an analytical solution of precisely three-dimensional problems of fluid motion is open. The first results on the use of the apparatus of four-dimensional mathematics for solving the three-dimensional model of the Navier-Stokes equations by the analytical method were obtained by the Kazakh mathematician Professor M.M. Abenov. After the author of this article with other researchers proved the theorem on the existence of a solution to the Cauchy problem for a three-dimensional model of filtration theory. This paper is devoted to the study of a three-dimensional model of the filtration theory in one of the spaces of four-dimensional numbers. The purpose of this article is to obtain an analytical solution of the three-dimensional Cauchy problem for the mathematical model of linear filtration model by the method of four-dimensional regular functions. In this study, a class of infinitely differentiable and bounded functions of the initial conditions of the Cauchy problem, satisfying the Cauchy-Riemann condition, with five degrees of freedom for a specific four-dimensional function is found, and also a class of infinitely differentiable and bounded solutions of this problem is found that satisfy the linear Darcy law.https://bm.kaznu.kz/index.php/kaznu/article/view/1083/667continuity equationdarcy’s lawfour-dimensional functioncauchy-riemann condition |
| spellingShingle | A. T. Rakhymova ONE CLASS OF SMOOTH BOUNDED SOLUTIONS TO THE CAUCHY PROBLEM FOR A THREE-DIMENSIONAL FILTRATION MODEL WITH DARCY'S LAW Вестник КазНУ. Серия математика, механика, информатика continuity equation darcy’s law four-dimensional function cauchy-riemann condition |
| title | ONE CLASS OF SMOOTH BOUNDED SOLUTIONS TO THE CAUCHY PROBLEM FOR A THREE-DIMENSIONAL FILTRATION MODEL WITH DARCY'S LAW |
| title_full | ONE CLASS OF SMOOTH BOUNDED SOLUTIONS TO THE CAUCHY PROBLEM FOR A THREE-DIMENSIONAL FILTRATION MODEL WITH DARCY'S LAW |
| title_fullStr | ONE CLASS OF SMOOTH BOUNDED SOLUTIONS TO THE CAUCHY PROBLEM FOR A THREE-DIMENSIONAL FILTRATION MODEL WITH DARCY'S LAW |
| title_full_unstemmed | ONE CLASS OF SMOOTH BOUNDED SOLUTIONS TO THE CAUCHY PROBLEM FOR A THREE-DIMENSIONAL FILTRATION MODEL WITH DARCY'S LAW |
| title_short | ONE CLASS OF SMOOTH BOUNDED SOLUTIONS TO THE CAUCHY PROBLEM FOR A THREE-DIMENSIONAL FILTRATION MODEL WITH DARCY'S LAW |
| title_sort | one class of smooth bounded solutions to the cauchy problem for a three dimensional filtration model with darcy s law |
| topic | continuity equation darcy’s law four-dimensional function cauchy-riemann condition |
| url | https://bm.kaznu.kz/index.php/kaznu/article/view/1083/667 |
| work_keys_str_mv | AT atrakhymova oneclassofsmoothboundedsolutionstothecauchyproblemforathreedimensionalfiltrationmodelwithdarcyslaw |