带反射的奇异积分微分方程的可解性与显解

Q3 Mathematics

Abstract and Applied Analysis Pub Date : 2024-05-16 DOI:10.1155/2024/5523649

A. S. Nagdy, KH. M. Hashem, H. E. H. Ebrahim

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引用次数: 0

摘要

本文讨论一类具有卷积核和反射的奇异积分微分方程。通过解析函数边界值问题理论和傅立叶分析理论，这类方程可以转化为带有节点和反射的黎曼边界值问题（即黎曼-希尔伯特问题）。对于这类问题，我们提出了一种不同于经典方法的新方法，通过这种方法可以获得显式解和可解条件。

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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The Solvability and Explicit Solutions of Singular Integral–Differential Equations with Reflection

This article deals with a classes of singular integral–differential equations with convolution kernel and reflection. By means of the theory of boundary value problems of analytic functions and the theory of Fourier analysis, such equations can be transformed into Riemann boundary value problems (i.e., Riemann–Hilbert problems) with nodes and reflection. For such problems, we propose a novel method different from classical one, by which the explicit solutions and the conditions of solvability are obtained.

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来源期刊

Abstract and Applied Analysis 数学-数学

CiteScore

2.30

自引率

0.00%

发文量

审稿时长

3.5 months

期刊介绍： Abstract and Applied Analysis is a mathematical journal devoted exclusively to the publication of high-quality research papers in the fields of abstract and applied analysis. Emphasis is placed on important developments in classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, optimization theory, and control theory. Abstract and Applied Analysis supports the publication of original material involving the complete solution of significant problems in the above disciplines. Abstract and Applied Analysis also encourages the publication of timely and thorough survey articles on current trends in the theory and applications of analysis.