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 Izv. IMI UdGU, 2016, Issue 2(48), Pages 73–81 (Mi iimi335)

Asymptotics of the Dirichlet problem solution for a ring with quadratic growths on the boundaries

D. A. Tursunov, U. Z. Erkebaev, E. A. Tursunov

Osh State University, ul. Lenina, 331, Osh, 723500, Kyrgyzstan

Abstract: The paper refers to the asymptotic behavior of the Dirichlet bisingular problem solution for a ring with quadratic growths on the boundaries. To construct the asymptotic expansion of the solution the authors apply the modified scheme of the classical method of boundary functions. The proposed method differs from the matching method by the fact that growing features of the outer expansion are in fact removed from it and with the help of an auxiliary asymptotic series are placed entirely in the internal expansion. An asymptotic expansion of the solution is a series of Puiseux, the basic term of the asymptotic expansion of the solution has a negative fractional degree of the small parameter. The resulting asymptotic expansion of the Dirichlet problem solution is justified by the maximum principle.

Keywords: asymptotic expansion of solution, bisingular perturbation, Dirichlet problem, Puiseux series, small parameter, method of boundary functions.

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UDC: 517.955.8
MSC: 35J15, 35J25, 35B25, 35B40, 35C20

Citation: D. A. Tursunov, U. Z. Erkebaev, E. A. Tursunov, “Asymptotics of the Dirichlet problem solution for a ring with quadratic growths on the boundaries”, Izv. IMI UdGU, 2016, no. 2(48), 73–81

Citation in format AMSBIB
\Bibitem{TurErkTur16} \by D.~A.~Tursunov, U.~Z.~Erkebaev, E.~A.~Tursunov \paper Asymptotics of the Dirichlet problem solution for a ring with quadratic growths on the boundaries \jour Izv. IMI UdGU \yr 2016 \issue 2(48) \pages 73--81 \mathnet{http://mi.mathnet.ru/iimi335} \elib{https://elibrary.ru/item.asp?id=27507185} 

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This publication is cited in the following articles:
1. K. G. Kozhobekov, D. A. Tursunov, “Asimptotika resheniya kraevoi zadachi, kogda predelnoe uravnenie imeet neregulyarnuyu osobuyu tochku”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:3 (2019), 332–340
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