Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (5): 1033-1040.

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

Siqian Qin,Zhengqiu Ling*(),Zewen Zhou   

  1. School of Mathematics and Statistics, Yulin Normal University, Guangxi Yulin 537000
  • Received:2018-09-05 Online:2019-10-26 Published:2019-11-08
  • Contact: Zhengqiu Ling
  • Supported by:
    the NSFC(11461076)


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 $\Omega \in {{\mathbb{R}}^{3}}$ 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

CLC Number: 

  • O175.2