Article
Article name About Liquid Filtration Under a Point Dam with a Vertical Weakly Permeable Film
Authors Yefimova I.A. Candidate of Physics and Mathematics, hol47@yandex.ru
Bibliographic description Efimova I. A. About Liquid Filtration Under a Point Dam with a Vertical Weakly Permeable Film // Scholarly Notes of Transbaikal State University. 2021. Vol. 16, No. 3. PP. 69-74. DOI: 10.21209/2658-7114-2021-16-3-69-74.
Section PROBLEMS OF MATHEMATICAL PHYSICS. ANALYTICAL METHODS
UDK 532.546
DOI 10.21209/2658-7114-2021-16-3-69-74
Article type
Annotation The problem of groundwater filtration under a point dam in a piecewise homogeneous porous medium in the presence of a weakly permeable film under the dam is considered. The filtration area is considered in the form of a vertical half-plane with a horizontal line of water courses. A weakly permeable film divides the filtration area into two quadrants with different constant permeability. By the convolution method of Fourier expansions, the solution of the problem is obtained explicitly. The influence of a weakly permeable film on the filtration process is investigated. It is shown that the presence of a weakly permeable film reduces the filtration rates in the downstream.
Key words boundary value problems in a piecewise homogeneous half-plane with a weakly permeable film, liquid filtration under a dam
Article information
References 1. Polubarinova-Kochina, P. Ya. The theory of groundwater movement. M: Nauka, 1977. (In Rus.) 2. Petrov, N. P. Constructions of currents under dams. Theoretical foundations of hydrodynamics. TGPI, 1979: 10-13. (In Rus.) 3. Efimova, I. A. Solution of the problem of fluid filtration under a point dam in a two-layer half-plane. Scientific notes of ZabGU, no. 4, p. 6-10, 2018. (In Rus.) 4. Efimova, I. A. Filtration of liquid under a point dam in a two-layer soil bounded from below by a water confinement. Scientific notes of ZabGU, no. 3, p. 6-11, 2019. (In Rus.) 5. Kholodovskii, S. E. The convolution method of Fourier expansions. The case of generalized transmission conditions of crack (screen) type in piecewise inhomogeneous media. Differential equations, no. 6, pp. 855-859, 2009. (In Engl.) 6. Arsenin, V. Ya. Methods of mathematical mathematics and special functions. M: Nauka, 1974. (In Rus.) 7. Andreeva, T. G. Mathematics: Special functions and some applications. SPb: RGGMU, 2013. (In Rus.) 8. Kholodovskii, S.E. On multilayer films on the boundary of a Half-Space. Mathematical notes, no. 3, pp. 426-431, 2016. (In Engl.) 9. Kholodovskii, S. E. Solution of boundary value problems for the La-place eguation in a ball bounded by a multilayer film. Differential equations, no. 7, pp. 891-899, 2017. (In Engl.) 10. Kholodovskii, S. E. Solution of boundary value problems in Cyl-inders with two-layer film inclusions. Journal of mathematical sciences, no. 1, pp. 55-59, 2018. (In Engl.)
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