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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-06-12 DOI:10.3934/math.20231300

Takiko Sasaki, Shuhei Takamatsu, H. Takamura

引用次数: 1

Abstract

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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具有空间导数的双线性项的一维波动方程经典解的寿命

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.