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Section
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Mathematics
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Title
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Asymptotics of the Dirichlet problem solution for a bisingular perturbed equation in the ring
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Author(-s)
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Tursunov D.A.ab,
Erkebaev U.Z.b
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Affiliations
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Ural State Pedagogical Universitya,
Osh State Universityb
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Abstract
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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.
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Keywords
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formal asymptotic expansion, Dirichlet problem, Airy function, Puiseux series, small parameter, method of boundary functions, bisingular perturbation
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UDC
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517.955.8
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MSC
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35J25, 35J75, 35J15
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DOI
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10.20537/vm150408
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Received
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13 October 2015
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Language
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Russian
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Citation
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Tursunov D.A., Erkebaev U.Z. Asymptotics of the Dirichlet problem solution for a bisingular perturbed equation in the ring, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2015, vol. 25, issue 4, pp. 517-525.
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References
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