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

doi:10.1016/S0252-9602(17)30052-8

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 XIA^1,2, Mingshu FAN³, Shan LI⁴

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

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

Anyin XIA, Mingshu FAN, Shan LI. BLOW-UP AND LIFE SPAN ESTIMATES FOR A CLASS OF NONLINEAR DEGENERATE PARABOLIC SYSTEM WITH TIME-DEPENDENT COEFFICIENTS[J].Acta mathematica scientia,Series B, 2017, 37(4): 974-984.

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

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