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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (9): 59-65.doi: 10.6040/j.issn.1671-9352.0.2020.675

• • 上一篇    

一类具有空变系数的非线性项的半线性双波动方程解的全局非存在性

欧阳柏平1,肖胜中2   

  1. 1.广州华商学院数据科学学院, 广东 广州 511300;2.广东农工商职业技术学院, 广东 广州 510507
  • 发布日期:2021-09-13
  • 作者简介:欧阳柏平(1979— ),男,硕士,讲师,研究方向为偏微分方程. E-mail:oytengfei79@tom.com
  • 基金资助:
    广东省普通高校创新团队资助项目(2020WCXTD008);广东财经大学华商学院校内资助项目(2020HSDS01);广州华商学院科研团队资助项目(2021HSKT01)

Global nonexistence of solutions to a class of semilinear double-wave equations with space-dependent coefficients on the nonlinearity

OUYANG Bai-ping1, XIAO Sheng-zhong2   

  1. 1. College of Data Science, Guangzhou Huashang College, Guangzhou 511300, Guangdong, China;
    2. Guangdong AIB Polytechnic College, Guangzhou 510507, Guangdong, China
  • Published:2021-09-13

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摘要： 考虑了一类具有空变系数的非线性项的半线性双波动方程解的爆破问题。运用微分不等式方法和迭代方法证明了半线性双波动方程柯西问题在非临界情况下解的全局非存在性,且给出了生命区间的上界估计。进一步推广了波动方程在高阶上柯西问题的有关结果。

关键词: 非线性项, 半线性双波动方程, 全局非存在性

Abstract: Blow-up of solutions to a class of semilinear double-wave equations with space-dependent coefficients on the nonlinearity is considered. By using the methods of differential inequalities and an iteration argument, the global nonexistence and the upper bound of the lifespan of solutions to the Cauchy problem for semilinear double-wave equations in the subcritical case are obtained, which generalize further the facts on the Cauchy problem for wave equations of high orders.

Key words: nonlinearity, semilinear double-wave equation, global nonexistence

中图分类号: 

  • O175.27
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