A Generalization of the Wiener–Hopf Method for an Equation in Two Variables with Three Unknown Functions

IF 1.9 4区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Applied Mathematics Pub Date : 2024-03-19 DOI:10.1137/23m1562445

Anastasia V. Kisil

引用次数: 0

Abstract

SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 464-476, April 2024.
Abstract. This manuscript presents an analytic solution to a generalization of the Wiener–Hopf equation in two variables and with three unknown functions. This equation arises in many applications, for example, when solving the discrete Helmholtz equation associated with scattering on a domain with perpendicular boundary. The traditional Wiener–Hopf method is suitable for problems involving boundary data on co-linear semi-infinite intervals, not for boundaries at an angle. This significant extension will enable the analytical solution to a new class of problems with more boundary configurations. Progress is made by defining an underlining manifold that links the two variables. This allows one to meromorphically continue the unknown functions on this manifold and formulate a jump condition. As a result the problem is fully solvable in terms of Cauchy-type integrals, which is surprising since this is not always possible for this type of functional equation.

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三未知函数两变量方程的维纳-霍普夫方法广义化

SIAM 应用数学杂志》，第 84 卷第 2 期，第 464-476 页，2024 年 4 月。摘要。本手稿介绍了两个变量和三个未知函数的维纳-霍普夫方程广义的解析解。该方程在许多应用中都会出现，例如在求解与垂直边界域上散射相关的离散亥姆霍兹方程时。传统的 Wiener-Hopf 方法适用于涉及共线半无限区间边界数据的问题，而不适用于角度边界问题。这一重大扩展将使我们能够对具有更多边界配置的新一类问题进行分析求解。通过定义一个连接两个变量的底线流形，取得了进展。这样，我们就可以在这个流形上对未知函数进行分形，并制定一个跳跃条件。因此，问题完全可以用考氏积分来解决，这一点令人惊讶，因为对于这类函数方程来说，这并不总是可能的。

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

SIAM Journal on Applied Mathematics 数学-应用数学

CiteScore

3.60

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.