scholarly journals Blow-Up Rate and Profile for a Degenerate Parabolic System Coupled via Nonlocal Sources

2006 ◽  
Vol 52 (10-11) ◽  
pp. 1387-1402 ◽  
Author(s):  
Sining Zheng ◽  
Lidong Wang
Keyword(s):  
Parabolic System ◽  
Blow Up ◽  
Degenerate Parabolic System ◽  
Nonlocal Sources ◽  
Degenerate Parabolic ◽  
Blow Up Rate

scholarly journals Blow-Up and Global Existence for a Degenerate Parabolic System with Nonlocal Sources

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Ling Zhengqiu ◽  
Wang Zejia
Keyword(s):  
Global Existence ◽  
Critical Exponent ◽  
Parabolic System ◽  
Blow Up ◽  
Nonnegative Solution ◽  
Degenerate Parabolic System ◽  
Nonlocal Sources ◽  
Nonnegative Solutions ◽  
Large Ball ◽  
Degenerate Parabolic

This paper investigates the blow-up and global existence of nonnegative solutions for a class of nonlocal degenerate parabolic system. By using the super- and subsolution techniques, the critical exponent of the system is determined. That is, ifPc=p1q1−(m−p2)(n−q2)<0, then every nonnegative solution is global, whereas ifPc>0, there are solutions that blowup and others that are global according to the size of initial valuesu0(x)andv0(x). WhenPc=0, we show that if the domain is sufficiently small, every nonnegative solution is global while if the domain large enough that is, if it contains a sufficiently large ball, there is no global solution.

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.

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