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Three Boundary Value Problems for Complex Partial Differential Equations in the Lens Domain

IF 0.7 4区 数学 Q3 MATHEMATICS, APPLIED
Computational Mathematics and Mathematical Physics Pub Date : 2024-07-18 DOI:10.1134/s0965542524700520
A. Darya, N. Taghizadeh
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Abstract

In this paper, we investigate some boundary value problems for the Cauchy–Riemann equations in the lens domain M. We apply the parqueting-reflection method for the domain to achieve the points of the complex plane. Then the Schwarz representation formula is constructed by the C-auchy–Pompeiu formula and an explicit solution for the Schwarz boundary value problem for the inhomogeneous Cauchy–Riemann equation on the domain is presented. We also discuss about the condition of solvability and by using the Schwarz boundary value problem, the homogeneous Ne-umann and the inhomogeneous Dirichlet boundary value problems are investigated.

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透镜域中复杂偏微分方程的三个边界值问题
摘要 本文研究了透镜域M中Cauchy-Riemann方程的一些边界值问题。然后通过 C-auchy-Pompeiu 公式构建了 Schwarz 表示公式，并给出了非均质 Cauchy-Riemann 方程在该域上的 Schwarz 边界值问题的显式解。我们还讨论了可解性条件，并利用 Schwarz 边界值问题研究了均相 Ne-umann 和非均相 Dirichlet 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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来源期刊
Computational Mathematics and Mathematical Physics
Computational Mathematics and Mathematical Physics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL
CiteScore
1.50
自引率
14.30%
发文量
125
审稿时长
4-8 weeks
期刊介绍： Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.
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