ASYMPTOTIC EXPANSIONS OF SOLUTIONS TO DIRICHLET PROBLEM FOR ELLIPTIC EQUATION WITH SINGULARITIES

被引：4

作者：

Tursunov, D. A. ^{[1
]}

Erkebaev, U. Z. ^{[2
]}

机构：

[1] Ural State Pedag Univ, Karl Liebknecht Str 9, Ekaterinburg 620151, Russia

[2] Osh State Univ, Lenin Str 331, Osh 723500, Kyrgyzstan

来源：

UFA MATHEMATICAL JOURNAL | 2016年 / 8卷 / 01期

关键词：

asymptotic expansion; Dirichlet problem; Airy function; modified Bessel functions; boundary functions;

D O I：

10.13108/2016-8-1-97

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper proposes an analogue of Vishik-Lyusternik-Vasileva-Imanalieva boundary functions method for constructing a uniform asymptotic expansion of solutions to bisingular perturbed problems. By means of this method we construct the uniform asymptotic expansion for the solution to the Dirichlet problem for bisingular perturbed second order elliptic equation with two independent variables in a circle. By the maximum principle we justify formal asymptotic expansion of the solution, that is, an estimate for the error term is established.

引用

页码：97 / 107

页数：11