估计自由边界问题中流动区域面积的精确公式

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-08-15 DOI:10.3103/s1066369x24700361

M. M. Alimov

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引用次数: 0

摘要

摘要提出了一种有效的技术，用于获得估算自由边界二维流体流动问题中流动区域面积的精确公式，该公式允许用椭圆函数精确求解。本文以有限深度液体表面的毛细管波问题为例，展示了该技术的有效性。这个例子的特点是流动区域具有镜面对称性，但该技术也可推广到流动区域具有其他对称性的情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Exact Formulas for Esimating the Area of Flow Regions in Free Boundary Problems

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Exact Formulas for Esimating the Area of Flow Regions in Free Boundary Problems

Abstract

An effective technique is proposed for obtaining exact formulas for estimating the area of flow regions in two-dimensional fluid flow problems with free boundaries, that allow an exact solution in terms of elliptic functions. The effectiveness of the technique is demonstrated using a specific example of the problem of capillary waves on the surface of a liquid of finite depth. This example is characterized by mirror symmetry of the flow region, but the technique can be generalized to the case of other symmetry of the flow region.

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来源期刊

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.