scholarly journals Global existence and blow-up of solutions for parabolic equations involving the Laplacian under nonlinear boundary conditions.

2021 ◽  
Keyword(s):  
Global Existence ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Nonlinear Boundary Conditions

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

2011 ◽  
Vol 54 (2) ◽  
pp. 309-324
Author(s):  
YONG-SHENG MI ◽  
CHUN-LAI MU ◽  
DENG-MING LIU
Keyword(s):  
Global Existence ◽  
Parabolic System ◽  
Parabolic Equations ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Nonlinear Boundary Conditions ◽  
Degenerate Parabolic Equations ◽  
Nonlinear Boundary Flux ◽  
Degenerate Parabolic ◽  
Boundary Flux

AbstractIn 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.

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