Lower bounds for the blow-up time of a nonlocal reaction-diffusion system with time-dependent coefficients

2021 ◽  
pp. 1-22
Author(s):  
Tae In Kwon ◽  
Zhong Bo Fang
Keyword(s):  
Lower Bounds ◽  
Blow Up ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Time Dependent ◽  
Nonlocal Reaction

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

Pulses and global bifurcations in a nonlocal reaction-diffusion system

1993 ◽  
Vol 48 (4) ◽  
pp. 2917-2923 ◽  
Author(s):  
Michael D. Graham ◽  
Usuf Middya ◽  
Dan Luss
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Global Bifurcations ◽  
Nonlocal Reaction
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