数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1033-1040.

• 论文 • 上一篇    

一类抛物方程爆破时间下界的确定方法与有效性分析

覃思乾, 凌征球, 周泽文   

  1. 玉林师范学院数学与统计学院 广西 玉林 537000
  • 收稿日期:2018-09-05 修回日期:2019-01-14 发布日期:2019-11-08
  • 通讯作者: 凌征球 E-mail:lingzq00@163.com
  • 基金资助:
    国家自然科学基金(11461076)

Some Methods for Determining the Lower Bound of Blow-up Time in a Parabolic Problem and Effectiveness Analysis

Qin Siqian, Ling Zhengqiu, Zhou Zewen   

  1. School of Mathematics and Statistics, Yulin Normal University, Guangxi Yulin 537000
  • Received:2018-09-05 Revised:2019-01-14 Published:2019-11-08
  • Supported by:
    Supported by the NSFC(11461076)

摘要: 利用能量估计方法与微分不等式技术,该文研究了一类具有可变非局部源项的牛顿渗流方程的Neumann边界值问题解的爆破现象,给出了解发生爆破时两个估计爆破时间下界的方法以及它们的有效性分析.

关键词: 牛顿渗流方程, 可变源, 爆破, 下界, 有效性

Abstract: In this paper, we consider the blow-up phenomenon to a type of Newtonian filtration equation with variable source subject to homogeneous Neumann boundary condition. We give two methods to determine the lower bound for blow-up time of solution in Ω ⊂ R3 if the solutions blow up by energy estimation method and diferential inequality technique. Moreover, the effectiveness of these methods are also discussed.

Key words: Newtonian filtration equation, Variable source, Blow-up, Lower bound, Effectiveness

中图分类号: 

  • O175.2