普鲁德曼-约翰逊方程解单调性的另一个计算机辅助证明

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED Japan Journal of Industrial and Applied Mathematics Pub Date : 2024-01-03 DOI:10.1007/s13160-023-00639-x

Yoshitaka Watanabe, Tomoyuki Miyaji

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引用次数: 0

摘要

本文提出了对二维流体流动具有代表性的普鲁德曼-约翰逊方程稳态解的存在性和单模性的计算机辅助证明。所提出的方法基于带区间算术的无穷维定点定理，是 Miyaji 和 Okamoto 的另一个证明（Jpn J Ind Appl Math 36:287-298, 2019）。验证结果表明了这两个证明的有效性。

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Another computer-assisted proof of unimodality of solutions for Proudman–Johnson equation

This paper presents a computer-assisted proof of the existence and unimodality of steady-state solutions for the Proudman–Johnson equation which is representative of two-dimensional fluid flow. The proposed approach is based on an infinite-dimensional fixed-point theorem with interval arithmetic, and is another proof by Miyaji and Okamoto (Jpn J Ind Appl Math 36:287–298, 2019). Verification results show the validity of both proofs.

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来源期刊

Japan Journal of Industrial and Applied Mathematics 数学-应用数学

CiteScore

1.50

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Japan Journal of Industrial and Applied Mathematics (JJIAM) is intended to provide an international forum for the expression of new ideas, as well as a site for the presentation of original research in various fields of the mathematical sciences. Consequently the most welcome types of articles are those which provide new insights into and methods for mathematical structures of various phenomena in the natural, social and industrial sciences, those which link real-world phenomena and mathematics through modeling and analysis, and those which impact the development of the mathematical sciences. The scope of the journal covers applied mathematical analysis, computational techniques and industrial mathematics.