Absorbing Sets of the Positive Solutions of the Schnackenberg Reaction-Diffusion System under Neumann Homogeneous Boundary Conditions

2009 ◽  
Author(s):  
S. Rionero ◽  
A. Tataranni
Keyword(s):  
Boundary Conditions ◽  
Positive Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Absorbing Sets

The Phenomenon of Quenching for a Reaction-Diffusion System with Non-Linear Boundary Conditions

2021 ◽  
Vol 88 (1-2) ◽  
pp. 155
Author(s):  
Halima Nachid ◽  
F. N'Gohisse ◽  
N'Guessan Koffi
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Reaction Diffusion ◽  
Nonlinear Boundary Conditions ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Lower And Upper Bounds ◽  
Linear Reaction ◽  
The One ◽  
Quenching Time

We study the quenching behavior of the solution of a semi- linear reaction-diffusion system with nonlinear boundary conditions. We prove that the solution quenches in finite time and its quenching time goes to the one of the solution of the differential system. We also obtain lower and upper bounds for quenching time of the solution.

scholarly journals Global Existence and Blowup for a Reaction-Diffusion System with Nonlocal Boundary Condition

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Jun Zhou
Keyword(s):  
Boundary Condition ◽  
Positive Solutions ◽  
Blow Up ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Rate Estimate ◽  
Blow Up Rate

This paper considers the singularity properties of positive solutions for a reaction-diffusion system with nonlocal boundary condition. The conditions on the existence and nonexistence of global positive solutions are given. Moreover, we establish the blow-up rate estimate for the blow-up solution.

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