Asymptotics of the Dirichlet problem solution for a ring with quadratic growths on the boundaries

The paper refers to the asymptotic behavior of the Dirichlet bisingular problem solution for a ring with quadratic growths on the boundaries. To construct the asymptotic expansion of the solution the authors apply the modified scheme of the classical method of boundary functions. 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. An asymptotic expansion of the solution is a series of Puiseux, the basic term of the asymptotic expansion of the solution has a negative fractional degree of the small parameter. The resulting asymptotic expansion of the Dirichlet problem solution is justified by the maximum principle.