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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2022, Number 7, Pages 58–72
DOI: https://doi.org/10.26907/0021-3446-2022-7-58-72 (Mi ivm9793) 		 
This article is cited in 5 scientific papers (total in 5 papers)

A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain

T. G. Ergasheva, Z. R. Tulakovab

a «Tashkent Institute of Irrigation and Agricultural Mechanization Engineers» National Research University, 39 Kari Niyazi str., Tashkent, 100000 Republic of Uzbekistan
b Fergana Branch of the Tashkent University of Information Technologies, 185 Mustakillik str., Fergana, 100118 Republic of Uzbekistan
Full-text PDF (487 kB) Citations (5)
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DOI: https://doi.org/10.26907/0021-3446-2022-7-58-72
Abstract: Solutions of the Dirichlet and Neumann problems for multidimensional singular elliptic equations in an infinite domain were found in explicit forms in recent works of the authors. In this paper, a problem with mixed conditions, which is a natural generalization of the previously considered Dirichlet and Neumann problems, is studied. In proving the existence of a unique solution to the problem posed, representation of the multiple Lauricella hypergeometric function at limiting values of the variables and a new formula for multiple improper integrals, which generalizes the well-known formula from the handbook of I.S. Gradshtein and I.M. Ryzhik, are used.
Keywords: Problem with mixed boundary conditions in an infinite domain, multidimensional elliptic equation with singular coefficients, fundamental solution, formula for the limit values of a hypergeometric function, Lauricella hypergeometric function of several variables.
Received: 28.09.2021
Revised: 11.11.2021
Accepted: 23.12.2021
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2022, Volume 66, Issue 7, Pages 51–63
DOI: https://doi.org/10.3103/S1066369X22070039
Document Type: Article
UDC: 517.946
Language: Russian
Citation: T. G. Ergashev, Z. R. Tulakova, “A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain”, Izv. Vyssh. Uchebn. Zaved. Mat., 2022, no. 7, 58–72; Russian Math. (Iz. VUZ), 66:7 (2022), 51–63
Citation in format AMSBIB
\Bibitem{ErgTul22}
\by T.~G.~Ergashev, Z.~R.~Tulakova
\paper A problem with mixed boundary conditions for a singular elliptic equation in an infinite domain
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2022
\issue 7
\pages 58--72
\mathnet{http://mi.mathnet.ru/ivm9793}
\crossref{https://doi.org/10.26907/0021-3446-2022-7-58-72}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2022
\vol 66
\issue 7
\pages 51--63
\crossref{https://doi.org/10.3103/S1066369X22070039}
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  • https://www.mathnet.ru/eng/ivm/y2022/i7/p58
    • This publication is cited in the following 5 articles:
    1. Otadavlat Nasriddinov, Jamoliddin Abdullayev, Dilnavoz Jo'rayeva, Nasiba Botirova, Oybek Maniyozov, Odilakhon Isomiddinova, V. Tsypko, S. Yekimov, A. Bieliatynskyi, “In biology, solving a problem coming to a differential equation in the maple program”, E3S Web of Conf., 508 (2024), 04006  crossref
    2. Bakhromjon Bozarov, Bakhtiyor Daliyev, Dadakhon Tukxtasinov, Otadavlat Nasriddinov, Makhfuza Ruzimatova, Nasiba Botirova, V. Tsypko, S. Yekimov, A. Bieliatynskyi, “Optimal cubature formulas for approximate integrals of functions defined on a sphere in three-dimensional space”, E3S Web of Conf., 508 (2024), 04016  crossref
    3. T. G. Ergashev, A. Hasanov, T. K. Yuldashev, “Some Infinite Expansions of the Lauricella Functions and Their Application in the Study of Fundamental Solutions of a Singular Elliptic Equation”, Lobachevskii J Math, 45:3 (2024), 1072  crossref
    4. A. A. Abdullaev, N. M. Safarbayeva, B. Kholkhodjaev, D. Bazarov, “Criteria for integro-differential modeling of plane-parallel flow of viscous incompressible fluid”, E3S Web of Conf., 401 (2023), 02018  crossref
    5. A. A. Abdullayev, M. Hidoyatova, B. A. Kuralov, D. Bazarov, “About one differential model of dynamics of groundwater”, E3S Web of Conf., 401 (2023), 02017  crossref
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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