Abstract

This article is devoted to the study of irregular singular points of the linear partial differential equations with holomorphic coefficients. In this paper we consider two important cases of differential equations. In the first case we consider partial differential equation with a special condition on the main symbol of the differential operator, in the second case considered Laplace equation on a manifold with cuspidal singularities. For these cases we construct asymptotics of solution with the help of resurgent analysis.

中文翻译：

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不规则奇异点附近的偏微分方程的渐近性

摘要

本文致力于研究具有全纯系数的线性偏微分方程的不规则奇异点。在本文中，我们考虑了两个重要的微分方程情况。在第一种情况下，我们考虑在微分算子的主要符号上具有特殊条件的偏微分方程，在第二种情况下，我们考虑具有尖峰奇异性的流形上的Laplace方程。对于这些情况，我们借助重新进行的分析来构造解的渐近性。