On asymptotic approximations of solutions of an equation with a small parameter

Il′in, A.; Lelikova, E.

doi:10.1090/S1061-0022-2011-01177-X

On asymptotic approximations of solutions of an equation with a small parameter
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by A. M. Il′in and E. F. Lelikova
Translated by: B. M. Bekker

St. Petersburg Math. J. 22 (2011), 927-939

DOI: https://doi.org/10.1090/S1061-0022-2011-01177-X

Published electronically: August 19, 2011

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Abstract:

A second order elliptic equation with a small parameter at one of the highest order derivatives is considered in a three-dimensional domain. The limiting equation is a collection of two-dimensional elliptic equations in two-dimensional domains depending on one parameter. By the method of matching of asymptotic expansions, a uniform asymptotic approximation of the solution of a boundary-value problem is constructed and justified up to an arbitrary power of a small parameter.

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