一类带卷积非线性项的波动方程耦合方程组解的破裂

兰州理工大学学报 ›› 2026, Vol. 52 ›› Issue (2): 151-157.

一类带卷积非线性项的波动方程耦合方程组解的破裂

亓明泽, 明森^*, 韩伟

中北大学数学学院, 山西太原 030051

收稿日期:2024-09-24 出版日期:2026-04-28 发布日期:2026-04-28
通讯作者: 明森(1987-),男,湖北随州人,博士后,副教授. Email:senming1987@163.com
基金资助:
山西省基础研究计划资助项目(20210302123045,20210302123021)

Blow-up of solutions for the coupled wave equations featuring convolution nonlinearities

QI Ming-ze, MING Sen, HAN Wei

Department of Mathematics, North University of China, Taiyuan 030051, China

Received:2024-09-24 Online:2026-04-28 Published:2026-04-28

摘要/Abstract

摘要： 在n维空间中探究一类包含卷积非线性项和尺度不变阻尼项波动方程耦合方程组的Cauchy问题.通过构造泛函并运用迭代方法进行研究,得到次临界和临界时小初值问题的解在有限时间内出现破裂,进而给出解的生命跨度的上界估计.

关键词: 波动方程组, 卷积非线性项, 迭代方法, 破裂, 生命跨度估计

Abstract: A class of Cauchy problem for coupled wave equations with convolutional nonlinear terms and scale invariant damping terms in n dimensional space was studied. By constructing the functionals andusing the iterative method, it is demonstrated that solutions to the small initial value problem in the sub-critical and critical cases will blow up at finite time. Furthermore, upper bound estimates for the lifespan of solutions is presented.

Key words: coupled wave equations, nonlinear convolution terms, iteration method, blow-up, lifespan estimates

中图分类号:

O175.29

亓明泽, 明森, 韩伟. 一类带卷积非线性项的波动方程耦合方程组解的破裂[J]. 兰州理工大学学报, 2026, 52(2): 151-157.

QI Ming-ze, MING Sen, HAN Wei. Blow-up of solutions for the coupled wave equations featuring convolution nonlinearities[J]. Journal of Lanzhou University of Technology, 2026, 52(2): 151-157.

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链接本文: https://journal.lut.edu.cn/CN/

https://journal.lut.edu.cn/CN/Y2026/V52/I2/151

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