scholarly journals Lower bounds for the blow-up time in a non-local reaction diffusion problem under nonlinear boundary conditions

2013 ◽  
Vol 57 (3-4) ◽  
pp. 926-931 ◽  
Author(s):  
Yan Liu
Keyword(s):  
Boundary Conditions ◽  
Lower Bounds ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Local Reaction ◽  
Reaction Diffusion ◽  
Nonlinear Boundary Conditions ◽  
Diffusion Problem ◽  
Non Local

scholarly journals Blow-Up Phenomena for Nonlinear Reaction-Diffusion Equations under Nonlinear Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Juntang Ding
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Global Solutions ◽  
Reaction Diffusion ◽  
Nonlinear Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Maximum Principles ◽  
Nonlinear Reaction

This paper deals with blow-up and global solutions of the following nonlinear reaction-diffusion equations under nonlinear boundary conditions:g(u)t=∇·au∇u+fu  in  Ω×0,T,  ∂u/∂n=bx,u,t  on  ∂Ω×(0,T),  u(x,0)=u0(x)>0,  in  Ω¯,whereΩ⊂RN  (N≥2)is a bounded domain with smooth boundary∂Ω. We obtain the conditions under which the solutions either exist globally or blow up in a finite time by constructing auxiliary functions and using maximum principles. Moreover, the upper estimates of the “blow-up time,” the “blow-up rate,” and the global solutions are also given.

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