华东师范大学学报（自然科学版） ›› 2023, Vol. 2023 ›› Issue (4): 24-34.doi: 10.3969/j.issn.1000-5641.2023.04.003

• 数学 • 上一篇    下一篇

一类具有导数型非线性项的弱耦合半线性双波动系统解的爆破

欧阳柏平()   

  1. 广州华商学院 数据科学学院, 广州　511300
  • 收稿日期:2021-07-27 出版日期:2023-07-25 发布日期:2023-07-25
  • 作者简介:欧阳柏平, 男, 讲师, 研究方向为偏微分方程. E-mail: oytengfei79@gdhsc.edu.cn
  • 基金资助:
    广东省普通高校重点项目(2019KZDXM042); 广东省普通高校创新团队项目(2020WCXTD008); 广东财经大学华商学院校内项目(2020HSDS01); 广州华商学院科研团队项目(2021HSKT01)

Blow-up of solutions to a class of weakly coupled semilinear double-wave systems with nonlinear terms of derivative type

Baiping OUYANG()   

  1. School of Data Science, Guangzhou Huashang College, Guangzhou　511300, China
  • Received:2021-07-27 Online:2023-07-25 Published:2023-07-25

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摘要：

考虑了一类具有导数型非线性项的弱耦合半线性双波动系统解的爆破现象. 通过选择合适的泛函以及运用迭代方法, 对 $p\ne q $ 时的弱耦合现象进行了深入研究, 当 $ p=q $ 时退化为单个导数型半线性双波动方程, 证明了非临界情况下其柯西问题解的全局非存在性. 同时, 导出了其解的生命跨度上界估计.

关键词: 导数型非线性项, 弱耦合半线性双波动系统, 爆破, 生命跨度

Abstract:

In this paper, blow-up of solutions to a class of weakly coupled semilinear double-wave systems with nonlinear terms of derivative type is considered. By choosing suitable functionals and using an iteration technique, the weakly coupled phenomena are studied in-depth for the case when $ p\ne q $ . For the case when $ p=q $ , the solution is degenerated to a single semilinear double-wave equation with a nonlinear term of derivative type. Furthermore, the nonexistence of global solutions to the Cauchy problem in the subcritical case is proven. Meanwhile, the upper bound estimate of the lifespan of solutions is also derived.

Key words: nonlinear term of derivative type, weakly coupled semilinear double-wave system, blow-up, lifespan

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