scholarly journals Blow-up analysis in a quasilinear parabolic system coupled via nonlinear boundary flux

2021 ◽  
pp. 1-13
Author(s):  
Pan Zheng ◽  
Zhonghua Xu ◽  
Zhangqin Gao
Keyword(s):  
Parabolic System ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Nonlinear Boundary Flux ◽  
Quasilinear Parabolic System ◽  
Blow Up Analysis ◽  
Boundary Flux ◽  
Quasilinear Parabolic

On the Critical Fujita Exponent for a Degenerate Parabolic System Coupled Via Nonlinear Boundary Flux

2008 ◽  
Vol 51 (3) ◽  
pp. 785-805 ◽  
Author(s):  
Jun Zhou ◽  
Chunlai Mu
Keyword(s):  
Initial Data ◽  
Boundary Conditions ◽  
Parabolic System ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Nonlinear Boundary Flux ◽  
Degenerate Parabolic System ◽  
Coupled Boundary Conditions ◽  
Degenerate Parabolic ◽  
Boundary Flux

AbstractIn this paper, we deal with the non-negative solutions of a degenerate parabolic system with nonlinear coupled boundary conditions and non-negative non-trivial compactly supported initial data. The critical Fujita exponents are given and the blow-up rates of the non-global solution are obtained.

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.

scholarly journals Blow-up analysis for a reaction-diffusion equation with gradient absorption terms

2021 ◽  
Vol 6 (12) ◽  
pp. 13774-13796
Author(s):  
Mengyang Liang ◽  
◽  
Zhong Bo Fang ◽  
Su-Cheol Yi ◽  
Keyword(s):  
Diffusion Equation ◽  
Differential Inequality ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Nonlinear Boundary Flux ◽  
Blow Up Analysis ◽  
Higher Dimensional ◽  
Boundary Flux

<abstract><p>This paper deals with the blow-up phenomena of solution to a reaction-diffusion equation with gradient absorption terms under nonlinear boundary flux. Based on the technique of modified differential inequality and comparison principle, we establish some conditions on nonlinearities to guarantee the solution exists globally or blows up at finite time. Moreover, some bounds for blow-up time are derived under appropriate measure in higher dimensional spaces $ \left({N \ge 2} \right). $</p></abstract>

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