奇数方程基本解的构建

IF 0.4 Q4 MATHEMATICS

Vestnik St Petersburg University-Mathematics Pub Date : 2024-01-24 DOI:10.1134/s1063454123040180

B. Yu. Irgashev

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引用次数: 0

摘要

摘要在以前的论文中，我们得到了一些具有多重特征的奇阶方程的三角型偏解，并研究了它们的一些性质。在本文中，我们首先得到了这些解在无穷远处的必要估计值，然后构造了矩形域中具有多个特征的奇阶方程的基本解（FS），作为这些特殊解的和。我们证明，FS 是矩形域中具有多重特征的非均质方程的解。反过来，FS 的知识又使我们能够构建一种潜在理论，进一步用于解决边界值问题。

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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Construction of Fundamental Solution for an Odd-Order Equation

Abstract

In previous papers, we obtained some delta-shaped partial solutions of odd-order equations with multiple characteristics and studied some of their properties. In this paper, we first obtain the necessary estimates at infinity for these solutions, and then construct a fundamental solution (FS) of an odd-order equation with multiple characteristics in a rectangular domain as the sum of these particular solutions. We show that the FS is a solution to an inhomogeneous equation with multiple characteristics in a rectangular domain. In turn, knowledge of FS allows us to construct a potential theory for its further use in solving boundary-value problems.

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来源期刊

Vestnik St Petersburg University-Mathematics MATHEMATICS-

CiteScore

0.70

自引率

50.00%

发文量

期刊介绍： Vestnik St. Petersburg University, Mathematics is a journal that publishes original contributions in all areas of fundamental and applied mathematics. It is the prime outlet for the findings of scientists from the Faculty of Mathematics and Mechanics of St. Petersburg State University. Articles of the journal cover the major areas of fundamental and applied mathematics. The following are the main subject headings: Mathematical Analysis; Higher Algebra and Numbers Theory; Higher Geometry; Differential Equations; Mathematical Physics; Computational Mathematics and Numerical Analysis; Statistical Simulation; Theoretical Cybernetics; Game Theory; Operations Research; Theory of Probability and Mathematical Statistics, and Mathematical Problems of Mechanics and Astronomy.