On a Method for Constructing the Riemann Function for Partial Differential Equations with a Singular Bessel Operator

被引：5

作者：

Karimov, Sh. T. ^{[1
]}

Oripov, Sh. A. ^{[1
]}

机构：

[1] Ferghana State Univ, Ferghana City 150100, Uzbekistan

来源：

LOBACHEVSKII JOURNAL OF MATHEMATICS | 2020年 / 41卷 / 06期

关键词：

Riemann function; Bessel operator; Erdelyi-Kober operators; Cauchy problem; singular hyperbolic equations;

D O I：

10.1134/S1995080220060128

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A linear second-order hyperbolic equation of two independent variables with a singular Bessel operator is considered. For particular types of such equations, a detailed literature review of known methods for constructing Riemann functions is given. It is shown that to construct the Riemann function for equations with a singular Bessel operator, we can use the Erdelyi-Kober transmutation operator. The Riemann function for the Euler-Poisson-Darboux differential equations is found in explicit form. In this paper, we give examples and an algorithm for constructing the Riemann function for second-order hyperbolic equations with the Bessel operator.

引用

页码：1087 / 1093

页数：7

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