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

Takiko Sasaki; Kerun Shao; Hiroyuki Takamura; Takiko Sasaki; Kerun Shao; Hiroyuki Takamura

doi:10.3934/math.2025754

AIMS Mathematics

2025, Volume 10, Issue 7: 16796-16803. doi: 10.3934/math.2025754

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Research article

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

1.
Department of Mathematical Engineering, Faculty of Engineering, Musashino University, 3-3-3 Ariake, Koto-ku, Tokyo 135-8181, Japan
2.
School of Mathematical Sciences, Zhejiang University, Hangzhou 310058, China
3.
Mathematical Institute, Tohoku University, Aoba, Sendai 980-8578, Japan

Received: 27 April 2025 Revised: 14 July 2025 Accepted: 17 July 2025 Published: 25 July 2025
MSC : 35B44, 35L71

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.
- nonlinear wave equation,
- blow-up,
- critical power,
- ordinary differential inequality,
- lifespan,
- slicing method
Citation: Takiko Sasaki, Kerun Shao, Hiroyuki Takamura. Slicing method for nonlinear integral inequalities related to critical nonlinear wave equations[J]. AIMS Mathematics, 2025, 10(7): 16796-16803. doi: 10.3934/math.2025754

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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.

References

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