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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (9): 133-136.doi: 10.6040/j.issn.1671-9352.0.2024.166

• • 上一篇    

一类四阶反应扩散方程解的爆破时刻下界

沈旭辉   

  1. 山西财经大学应用数学学院, 山西 太原 030006
  • 发布日期:2025-09-10
  • 基金资助:
    国家自然科学基金资助项目(61473180);山西省青年科技研究基金资助项目(20210302124533)

Lower bound for the blow-up time of solutions to a class of fourth-order reaction-diffusion equations

SHEN Xuhui   

  1. School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006, Shanxi, China
  • Published:2025-09-10

摘要: 研究一类四阶反应扩散方程解的爆破现象,通过推导适用于高维空间的Sobolev不等式,构造合适的辅助函数和利用微分不等式技巧,给出方程解的爆破时刻下界。

关键词: 四阶反应扩散方程, 爆破, 爆破时刻下界

Abstract: The blow-up phenomenon of solutions to a class of fourth-order reaction-diffusion equations are considered. By deriving a Sobolev inequality suitable for high-dimensional spaces, constructing appropriate auxiliary functions, and employing differential inequality techniques, a lower bound for the blow-up time of solutions is provided.

Key words: fourth-order reaction-diffusion equation, blow-up, lower bound for the blow-up time

中图分类号: 

  • O175
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