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Research Article | Open Access

Slicing method for nonlinear integral inequalities related to critical nonlinear wave equations

Takiko Sasaki1, Kerun Shao2, Hiroyuki Takamura3( )
Department of Mathematical Engineering, Faculty of Engineering, Musashino University, 3-3-3 Ariake, Koto-ku, Tokyo 135-8181, Japan
School of Mathematical Sciences, Zhejiang University, Hangzhou 310058, China
Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan
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Abstract

This paper is devoted to a simple and short proof on the sharp upper bound of lifespan of classical solutions to wave equations with the critical power nonlinearities of spatial derivatives of the unknown function. Such a proof is so-called "slicing method", which may help us to extend the result for various equations and systems.

Keywords

nonlinear wave equationblow-upcritical powerordinary differential inequalitylifespanslicing method
CLC number: 35B44, 35L71

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AIMS Mathematics
Volume 10 Issue 7,
July 2025
Pages 16796-16803
DOI: 10.3934/math.2025754

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Cite this article:
Sasaki T, Shao K, Takamura H. Slicing method for nonlinear integral inequalities related to critical nonlinear wave equations. AIMS Mathematics, 2025, 10(7): 16796-16803. https://doi.org/10.3934/math.2025754

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Received: 27 April 2025
Revised: 14 July 2025
Accepted: 17 July 2025
Published: 15 July 2025
©2025 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)