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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2015, Volume 25, Issue 4, Pages 517–525 (Mi vuu505)  

This article is cited in 4 scientific papers (total in 4 papers)

MATHEMATICS

Asymptotics of the Dirichlet problem solution for a bisingular perturbed equation in the ring

D. A. Tursunova, U. Z. Erkebaevb

a Department of Higher Mathematics, Ural State Pedagogical University, ul. Karl Liebknecht, 9, Yekaterinburg, 620151, Russia
b Department of Algebra and Geometry, Osh State University, ul. Lenina, 331, Osh, 723500, Kyrgyzstan

Abstract: The paper refers to the asymptotic behavior of the Dirichlet problem solution for a bisingular perturbed elliptic second-order equation with two independent variables in the ring. To construct the asymptotic expansion of the solution the authors apply the modified scheme of the method of boundary functions by Vishik–Lyusternik–Vasil'eva–Imanaliev. 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, and from the classical method of boundary functions by the fact that boundary functions have power-law decrease, not exponential. An asymptotic expansion of the solution is a series of Puiseux. The resulting asymptotic expansion of the Dirichlet problem solution is justified by the maximum principle.

Keywords: formal asymptotic expansion, dirichlet problem, airy function, Puiseux series, small parameter, method of boundary functions, bisingular perturbation.

Funding Agency Grant Number
Ministry of Education and Science of Kyrgyz Republic


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Document Type: Article
UDC: 517.955.8
MSC: 35J25, 35J75, 35J15
Received: 13.10.2015

Citation: D. A. Tursunov, U. Z. Erkebaev, “Asymptotics of the Dirichlet problem solution for a bisingular perturbed equation in the ring”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 25:4 (2015), 517–525

Citation in format AMSBIB
\Bibitem{TurErk15}
\by D.~A.~Tursunov, U.~Z.~Erkebaev
\paper Asymptotics of the Dirichlet problem solution for a~bisingular perturbed equation in the ring
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2015
\vol 25
\issue 4
\pages 517--525
\mathnet{http://mi.mathnet.ru/vuu505}
\elib{http://elibrary.ru/item.asp?id=25109972}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. A. Tursunov, U. Z. Erkebaev, “Asimptotika resheniya bisingulyarno vozmuschennoi zadachi Dirikhle v koltse s kvadratichnym rostom na granitse”, Vestn. Yuzhno-Ur. un-ta. Ser. Matem. Mekh. Fiz., 8:2 (2016), 52–61  mathnet  crossref  elib
    2. D. A. Tursunov, U. Z. Erkebaev, E. A. Tursunov, “Asimptotika resheniya zadachi Dirikhle dlya koltsa s kvadratichnymi rostami na granitsakh”, Izv. IMI UdGU, 2016, no. 2(48), 73–81  mathnet  elib
    3. D. A. Tursunov, “Obobschennyi metod pogranfunktsii dlya bisingulyarnykh zadach v kruge”, Tr. IMM UrO RAN, 23, no. 2, 2017, 239–249  mathnet  crossref  elib
    4. D. A. Tursunov, “Asymptotic solving linear bisingular problems with additional boundary layer”, Russian Math. (Iz. VUZ), 62:3 (2018), 60–67  mathnet  crossref  isi
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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