Construction of Normal-Regular Solutions of Inhomogeneous System of Partial Differential Equations of Second Order

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-02-27 DOI:10.1002/mma.10828

Meiramgul Talipova

引用次数: 0

Abstract

In this paper, we consider an inhomogeneous system of second-order partial differential equations with regular singularities at the point (0, 0). The Frobenius-Latysheva method is used to find normally regular solutions. A universal approach to constructing solutions in the vicinity of regular singularities has been developed, the number of linearly independent partial solutions has been determined, and compatibility and integrability conditions have been investigated. Concrete examples demonstrate the use of the method of uncertain coefficients to obtain partial solutions of inhomogeneous systems.

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二阶非齐次偏微分方程组正正则解的构造

本文研究了在点（0,0）处具有正则奇异点的二阶偏微分方程组的非齐次问题。Frobenius-Latysheva方法用于求正解。给出了构造正则奇点附近解的一种通用方法，确定了线性无关部分解的个数，并研究了相容和可积条件。具体实例说明了利用不确定系数法求解非齐次系统的部分解。

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

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.