Asymptotic Solution of a Singularly Perturbed Cauchy Problem in the Presence of a Rational Simple Turning Point

被引：0

作者：

A. G. Eliseev ^{[1
]}

T. A. Ratnikova ^{[1
]}

机构：

[1] National Research University “Moscow Energy Institute”, Moscow

来源：

Journal of Mathematical Sciences | 2025年 / 288卷 / 1期

关键词：

34E20; asymptotic solution; regularization method; singularly perturbed Cauchy problem; turning point;

D O I：

10.1007/s10958-025-07666-8

中图分类号：

学科分类号：

摘要：

In this paper, based on S. A. Lomov’s regularization method, we construct an asymptotic solution of a singularly perturbed Cauchy problem in the case of violation of the stability conditions for the spectrum of the limit operator. In particular, we consider the problem with a “simple” turning point, i.e., where one eigenvalue vanishes for t = 0 and has the form tm/n (the limit operator is discretely irreversible). © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.

引用

页码：80 / 86

页数：6

共 4 条

[1]

Eliseev A.G., Lomov S.A., Theory of singular perturbations in the case of spectral singularities of the limit operator, Mat. Sb, 131, 173, pp. 544-557, (1986)

[2]

Lioville J., Second memoire sur le développement des fonctions en séries dont divers termes sont assujettis, à une même équation, J. Math. Pure Appl, 2, pp. 16-35, (1837)

[3]

Lomov S.A., Introduction to the General Theory of Singular Perturbations, (1981)

[4]

Tursunov D.A., Kozhbekov K.G., Asymptotics of solutions of singularly perturbed differential equations with fractional turning point, Izv. Irkutsk. Univ, 21, pp. 108-121, (2017)

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