Abstract

The aim of the research is the development of the asymptotic method of boundary functions to Robin problem for a ring with regularly singular boundary. This work is devoted to constructing complete asymptotic expansions of the solutions of Robin problem for singular perturbed inhomogeneous linear second order elliptic equation with regularly singular boundary. Singularities of the equation: the presence of a small parameter at the Laplace operator and the corresponding unperturbed (limit) the differential equation of first order has a singularity at the border ring. Bisingularly problems of the Robin studied in the ring. Full asymptotic expansion of the solution of bisingularly problems constructed by modification method of boundary functions. The resulting solutions are asymptotic in the sense Erdei. The resulting asymptotic expansions of the solutions of boundary value problems justified by the principle of maximum.

中文翻译：

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具有规则奇异边界的圆环的罗宾问题解的渐近性

摘要

研究的目的是发展具有规则奇异边界环的Robin问题的边界函数渐近方法。这项工作致力于构造奇异摄动具有规则奇异边界的奇异摄动线性二阶椭圆方程罗宾问题解的完整渐近展开。方程的奇异性：在Laplace算子上存在一个小参数，以及相应的一阶微分方程的无扰动（极限），在边界环处具有奇异性。罗宾在环上研究了奇异的问题。通过边界函数的修正方法构造的双奇异问题解的完全渐近展开。所得的解在Erdei的意义上是渐近的。