Geodesic
Asymptotics of the Dirichlet problem solution for a bisingular perturbed equation in the ring
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 4, pp. 517-525 Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: formal asymptotic expansion, dirichlet problem, airy function, small parameter, method of boundary functions
Mots-clés : Puiseux series, bisingular perturbation. 
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     title = {Asymptotics of the {Dirichlet} problem solution for a~bisingular perturbed equation in the ring},
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D. A. Tursunov; U. Z. Erkebaev. Asymptotics of the Dirichlet problem solution for a bisingular perturbed equation in the ring. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 25 (2015) no. 4, pp. 517-525. http://geodesic.mathdoc.fr/item/VUU_2015_25_4_a7/

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