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Research Article | Open Access

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

Takiko Sasaki1,3, Shu Takamatsu2, Hiroyuki Takamura3( )
Department of Mathematical Engineering, Faculty of Engineering, Musashino University, 3-3-3 Ariake, Koto-ku, Tokyo 135-8181, Japan
Master course, Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan
Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan
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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.

Keywords

semilinear wave equationone dimensionclassical solutionlifespan
CLC number: primary 35L71, secondary 35B44

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AIMS Mathematics
Volume 8 Issue 11,
November 2023
Pages 25477-25486
DOI: 10.3934/math.20231300

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Cite this article:
Sasaki T, Takamatsu S, Takamura H. The lifespan of classical solutions of one dimensional wave equations with semilinear terms of the spatial derivative. AIMS Mathematics, 2023, 8(11): 25477-25486. https://doi.org/10.3934/math.20231300

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Received: 23 June 2023
Revised: 17 August 2023
Accepted: 23 August 2023
Published: 15 November 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)