利用等边三角形中的混合边界条件求解修正的亥姆霍兹方程

Q1 Mathematics Partial Differential Equations in Applied Mathematics Pub Date : 2024-09-01 Epub Date: 2024-08-24 DOI:10.1016/j.padiff.2024.100895

Pratul Gadagkar , Subhash Kendre , Pooja Paratane

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引用次数: 0

摘要

修正的亥姆霍兹方程 qxx+qyy-4β2q=0 是经典数学物理的基本方程之一。在本文中，我们得到了等边三角形中修正亥姆霍兹方程的边界值问题解。本文考虑了与解的对称性有关的附加混合边界条件。我们分析了全局关系，并绕过黎曼-希尔伯特方法，仅使用代数技术获得了修正亥姆霍兹方程的显式解。这个解被应用于扩散受限的凝聚问题，A+A⇌A。

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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Solution of the modified Helmholtz equation using mixed boundary conditions in an equilateral triangle

The modified Helmholtz equation $q_{x x} + q_{y y} - 4 β^{2} q = 0$ , is one of the basic equations of classical mathematical physics. In this paper we have obtained the solution of the boundary-value problems for the modified Helmholtz equation in an equilateral triangle. An additional mixed boundary condition related to the symmetry of the solution is taken into consideration. We have analysed the Global relation and only used the algebraic techniques to obtain the explicit solution of modified Helmholtz equation bypassing the Riemann Hilbert approach. This solution is applied to the problem of diffusion-limited coalescence, $A + A ⇌ A$ .