Acta mathematica scientia,Series B ›› 2017, Vol. 37 ›› Issue (4): 974-984.doi: 10.1016/S0252-9602(17)30052-8

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BLOW-UP AND LIFE SPAN ESTIMATES FOR A CLASS OF NONLINEAR DEGENERATE PARABOLIC SYSTEM WITH TIME-DEPENDENT COEFFICIENTS

Anyin XIA1,2, Mingshu FAN3, Shan LI4   

  1. 1. School of Science, Xihua University, Chengdu 610039, China;
    2. Department of Mathematics, Sichuan University, Chengdu 610065, China;
    3. Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, China;
    4. Business School, Sichuan University, Chengdu 610065, China
  • Received:2016-05-13 Revised:2016-08-07 Online:2017-08-25 Published:2017-08-25
  • Contact: Shan LI,E-mail:lishan@scu.edu.cn E-mail:lishan@scu.edu.cn
  • About author:Anyin XIA,E-mail:xay004@163.com;Mingshu FAN,E-mail:fanmingshu@hotmail.com
  • Supported by:

    This work was supported in part by NSFC (11571243), Sichuan Youth Science and Technology Foundation (2014JQ0003), Fundamental Research Funds for the Central Universities (2682016CX116) and Project of Education Department of Sichuan Province (14226423).

Abstract:

This paper deals with the singularity and global regularity for a class of nonlinear porous medium system with time-dependent coefficients under homogeneous Dirichlet boundary conditions. First, by comparison principle, some global regularity results are established. Secondly, using some differential inequality technique, we investigate the blow-up solution to the initial-boundary value problem. Furthermore, upper and lower bounds for the maximum blow-up time under some appropriate hypotheses are derived as long as blow-up occurs.

Key words: porous medium systems, Dirichlet boundary conditions, global existence, blowup, upper and lower bounds

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