scholarly journals Dirichlet boundary conditions can prevent blow-up in reaction-diffusion equations and systems

2005 ◽  
Vol 14 (1) ◽  
pp. 63-74 ◽  
Author(s):  
Juan-Luis Vázquez ◽  
Hirokazu Ninomiya ◽  
Marek Fila
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Blow Up ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Dirichlet Boundary Conditions ◽  
Diffusion Equations

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.

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