半离散基尔霍夫方程的全局可解性

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-08-30 DOI:10.1002/mma.10453

Fumihiko Hirosawa

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引用次数: 0

摘要

对于本身难以分析的偏微分方程，考虑离散化问题是很有效的。基尔霍夫方程初值问题的全局可解性至今仍未解决，除非初值是一个特别受限的类别。在本文中，我们证明了半离散基尔霍夫方程的全局可解性，它是通过对基尔霍夫方程进行空间变量离散化而得到的。

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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Global solvability for semidiscrete Kirchhoff equation

It is effective to consider discretized problems for partial differential equations that are difficult to analyze themselves. The global solvability of the initial value problem of the Kirchhoff equation is still unsolved except in cases where the initial value is a specially restricted class. In this paper, we prove the global solvability of the semidiscrete Kirchhoff equation, which is obtained by discretizing the Kirchhoff equation with respect to spatial variables.

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.