Asymptotics of the Solution of the Cauchy Problem with an Unstable Spectrum and Prolonging Loss of Stability

IF 0.8 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI:10.1134/s1995080224600845

D. A. Tursunov, A. S. Sadieva, K. G. Kozhobekov, E. A. Tursunov

引用次数: 0

Abstract

The article is devoted to construct a complete asymptotic expansion of the solution to the Cauchy problem for a linear analytical system of singularly perturbed ordinary differential equations of the first order. The peculiarities of the Cauchy problem are that a small parameter is present in front of the derivative, and the stability conditions are violated in the region under consideration. By modifying the method of boundary functions, a formal asymptotic expansion of the solution to the Cauchy problem is constructed. The remainder term of the expansion is estimated by the idea of L.S. Pontryagin entering the complex plane.

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具有不稳定频谱和长期失稳的考奇问题解的渐近性

摘要本文致力于构建一阶奇异扰动常微分方程线性解析系统的 Cauchy 问题解的完整渐近展开。Cauchy 问题的特殊性在于导数前存在一个小参数，并且在所考虑的区域内违反了稳定性条件。通过修改边界函数方法，构建了 Cauchy 问题解的形式渐近展开。根据 L.S. Pontryagin 进入复平面的思想，对扩展的余项进行了估计。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Lobachevskii Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

42.90%

发文量

127

期刊介绍： Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.