The Riemann problem on a ray for generalized analytic functions with a singular line

被引：1

作者：

Shabalin, P. L. ^{[1
]}

Faizov, R. R. ^{[1
]}

机构：

[1] Kazan State Univ Architecture & Engn, 1 Zelenaya St, Kazan 420043, Russia

来源：

IZVESTIYA OF SARATOV UNIVERSITY MATHEMATICS MECHANICS INFORMATICS | 2023年 / 23卷 / 01期

关键词：

Riemann problem; generalized analytical functions; infinite index; integer functions of refined zero order; BOUNDARY-VALUE PROBLEM; INTEGRAL-REPRESENTATIONS; SYSTEM; EQUATION;

D O I：

10.18500/1816-9791-2023-23-1-58-69

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study an inhomogeneous Riemann boundary value problem with a finite index and a boundary condition on a ray for a generalized Cauchy - Riemann equation with a singular coefficient. For the solution of this problem, we derived a formula for the general solution of the generalized Cauchy - Riemann equation under constraints that led to an infinite index of logarithmic order of the accompanying problem for analytical functions. We have obtained a formula for the general solution of the Riemann problem and conducted a complete study of the existence and the number of solutions of a boundary value problem for generalized analytic functions with a singular line.

引用

页码：58 / 69

页数：12

共 50 条

[41] A Riemann-Hilbert approach to the inverse problem for the Stark operator on the line
Its, A.
Sukhanov, V.
INVERSE PROBLEMS, 2016, 32 (05)
[42] Riemann-Hilbert Problems for Hardy Space of Meta-Analytic Functions on the Unit Disc
Ku, Min
He, Fuli
Wang, Ying
COMPLEX ANALYSIS AND OPERATOR THEORY, 2018, 12 (02) : 457 - 474
[43] Riemann boundary-value problem for doubly-periodic bianalytic functions
Han, Huili
Liu, Hua
Wang, Yufeng
BOUNDARY VALUE PROBLEMS, 2018,
[44] INVESTIGATION OF THE RIEMANN BOUNDARY PROBLEM FOR VECTOR FUNCTIONS. APPLICATION IN MATHEMATICAL PHYSICS
Voronin, A. F.
SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2011, 8 : C74 - C84
[45] THE RIEMANN PROBLEM AND THE LIMIT SOLUTIONS AS MAGNETIC FIELD VANISHES TO MAGNETOGASDYNAMICS FOR GENERALIZED CHAPLYGIN GAS
Chen, Jianjun
Sheng, Wancheng
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2018, 17 (01) : 127 - 142
[46] A Random Choice Method based on the Generalized Riemann Problem for the Euler equations in gas dynamics
Zhang, Qinglong
Sheng, Wancheng
JOURNAL OF COMPUTATIONAL PHYSICS, 2021, 441
[47] Lower and upper functions in a singular Dirichlet problem with o-Laplacian
Rachunkova, I.
Stryja, J.
MATHEMATICAL NOTES, 2015, 97 (3-4) : 588 - 597
[48] Riemann boundary value problems for multiplicative doubly quasi-periodic meta-analytic functions
Duan, Ping
Ku, Min
Wang, Ying
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2023, 68 (06) : 892 - 917
[49] Hyperbolic systems of conservation laws with Lipschitz continuous flux-functions: The Riemann problem
Joaquim Correia
Philippe G. LeFloch
Mai Duc Thanh
Boletim da Sociedade Brasileira de Matemática - Bulletin/Brazilian Mathematical Society, 2001, 32 : 271 - 301
[50] On a Riemann Boundary Value Problem in the Half-plane in the Class of Weighted Continuous Functions
H. M. Hayrapetyan
S. A. Aghekyan
Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences), 2019, 54 : 79 - 89

← 1 2 3 4 5 →