Geodesic
On asymptotic approximations of solutions of an equation with a~small parameter
Algebra i analiz, Tome 22 (2010) no. 6, pp. 109-126.

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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.
Keywords: asymptotic, boundary value problem, small parameter, matching of asymptotic expansions. 
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A. M. Il'in; E. F. Lelikova. On asymptotic approximations of solutions of an equation with a~small parameter. Algebra i analiz, Tome 22 (2010) no. 6, pp. 109-126. http://geodesic.mathdoc.fr/item/AA_2010_22_6_a5/

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