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GLOBAL EXISTENCE AND BLOW-UP FOR A DOUBLY DEGENERATE PARABOLIC EQUATION SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS

Published online by Cambridge University Press:  12 December 2011

YONG-SHENG MI ,
CHUN-LAI MU  and
DENG-MING LIU
YONG-SHENG MI
Affiliation:
College of Mathematics and Statistics, Chongqing University, Chongqing 400044, PR China; College of Mathematics and Computer Sciences, Yangtze Normal University, Fuling 408100, Chongqing, PR China e-mail: miyongshen@163.com
CHUN-LAI MU
Affiliation:
College of Mathematics and Statistics, Chongqing University, Chongqing 400044, PR China e-mail: chunlaimu@yahoo.com.cn
DENG-MING LIU
Affiliation:
College of Mathematics and Statistics, Chongqing University, Chongqing 400044, PR China e-mail: liudengming08@163.com
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Abstract

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In this paper, we deal with the global existence and blow-up of solutions to a doubly degenerative parabolic system with nonlinear boundary conditions. By constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions for global existence of non-negative solutions, which extend the recent results of Zheng, Song and Jiang (S. N. Zheng, X. F. Song and Z. X. Jiang, Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux, J. Math. Anal. Appl. 298 (2004), 308–324), Xiang, Chen and Mu (Z. Y. Xiang, Q. Chen, C. L. Mu, Critical curves for degenerate parabolic equations coupled via nonlinear boundary flux, Appl. Math. Comput. 189 (2007), 549–559) and Zhou and Mu (J. Zhou and C. L Mu, On critical Fujita exponents for degenerate parabolic system coupled via nonlinear boundary flux, Pro. Edinb. Math. Soc. 51 (2008), 785–805) to more general equations.

Keywords

35K5535K6535B40
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 2 , May 2012 , pp. 309 - 324
Copyright
Copyright © Glasgow Mathematical Journal Trust 2011

References

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