SOLVING CONVOLUTION SINGULAR INTEGRAL EQUATIONS WITH REFLECTION AND TRANSLATION SHIFTS UTILIZING RIEMANN-HILBERT APPROACH

Pingrun Li; Songwei Bai; Meng Sun; Na Zhang

doi:10.11948/20210214

2022 Volume 12 Issue 2

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Pingrun Li, Songwei Bai, Meng Sun, Na Zhang. SOLVING CONVOLUTION SINGULAR INTEGRAL EQUATIONS WITH REFLECTION AND TRANSLATION SHIFTS UTILIZING RIEMANN-HILBERT APPROACH[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 551-567. doi: 10.11948/20210214

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Pingrun Li, Songwei Bai, Meng Sun, Na Zhang. SOLVING CONVOLUTION SINGULAR INTEGRAL EQUATIONS WITH REFLECTION AND TRANSLATION SHIFTS UTILIZING RIEMANN-HILBERT APPROACH[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 551-567. doi: 10.11948/20210214

SOLVING CONVOLUTION SINGULAR INTEGRAL EQUATIONS WITH REFLECTION AND TRANSLATION SHIFTS UTILIZING RIEMANN-HILBERT APPROACH

1.
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Corresponding author: Email address: lipingrun@163.com(P. Li)

Abstract

Abstract

In this paper, method of solution for some kinds of convolution singular integral equations with reflection will be discussed in class {0}. By means of the theory of Fourier analysis and the theory of boundary value problems of analytic functions, such equations can be transformed into Riemann boundary value problems (i.e., Riemann-Hilbert problems) with nodes and reflection, or a system of linear algebraic equations. In spite of the classical method for solution, we are to give a new method, by which analytic solutions and conditions of Noether solvability are obtained respectively. At the end of this paper, we propose two kinds of convolution singular integral equations with reflections and a finite set of translation shifts.
- Singular integral equations of convolution type, Riemann-Hilbert problems /
- Noether theory /
- reflection /
- translation shifts
MSC: 45E10, 45E05, 30E25

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References

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