Maqola

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

Yongsheng MiCollege 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:Chunlai MuCollege of Mathematics and Statistics, Chongqing University, Chongqing 400044, PR China e-mail:Dengming LiuCollege of Mathematics and Statistics, Chongqing University, Chongqing 400044, PR China e-mail:

2011en

ABI

Annotatsiya

Abstract 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.

Hali tarjima qilinmagan

Identifikatorlar

DOI: 10.1017/s0017089511000619

Iqtiboslar va manbalar

2 ta iqtibos0 ta foydalanilgan manba

Koʻrsatkichlar — AkademScholar