具有空间导数的双线性项的一维波动方程经典解的寿命

IF 1.8 3区数学 Q1 MATHEMATICS AIMS Mathematics Pub Date : 2023-06-12 DOI:10.3934/math.20231300

Takiko Sasaki, Shuhei Takamatsu, H. Takamura

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引用次数: 1

摘要

本文致力于具有未知函数空间导数的双线性项的一维波动方程初值问题的小经典解的寿命估计。这个结果和时间导数的双线性项的结果是一样的，这是很自然的。但他们的证明之间有很多不同之处。此外，研究这一问题有意义，因为它可能有助于我们在不久的将来研究其爆炸边界。

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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The lifespan of classical solutions of one dimensional wave equations with semilinear terms of the spatial derivative

This paper is devoted to the lifespan estimates of small classical solutions of the initial value problems for one dimensional wave equations with semilinear terms of the spatial derivative of the unknown function. It is natural that the result is same as the one for semilinear terms of the time-derivative. But there are so many differences among their proofs. Moreover, it is meaningful to study this problem in the sense that it may help us to investigate its blow-up boundary in the near future.

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来源期刊

AIMS Mathematics Mathematics-General Mathematics

CiteScore

3.40

自引率

13.60%

发文量

769

审稿时长

90 days

期刊介绍： AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.