scholarly journals Existence and Nonexistence of Global Solutions in Time for a Reaction-Diffusion System with Inhomogeneous Terms

2008 ◽  
Vol 51 (1) ◽  
pp. 17-37 ◽  
Author(s):  
Takefumi Igarashi ◽  
Noriaki Umeda
Keyword(s):  
Global Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Existence And Nonexistence

scholarly journals Global solutions of a strongly coupled reaction-diffusion system with different diffusion coefficients

2005 ◽  
Vol 2005 (1) ◽  
pp. 23-36 ◽  
Author(s):  
L. W. Somathilake ◽  
J. M. J. J. Peiris
Keyword(s):  
Semigroup Theory ◽  
Global Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Reaction Diffusion Equations ◽  
Diffusion System ◽  
Strongly Coupled ◽  
Diffusion Rates ◽  
Coupled Reaction ◽  
Growth Of Solutions

We deal with a mathematical model for a four-component chemical reaction-diffusion process. The model is described by a system of strongly coupled reaction-diffusion equations with different diffusion rates. The existence of the global solution of this reaction-diffusion system in unbounded domain is proved by using semigroup theory and estimates on the growth of solutions.

scholarly journals Global Solutions for an -Component System of Activator-Inhibitor Type

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
S. Abdelmalek ◽  
A. Gouadria ◽  
A. Youkana
Keyword(s):  
Lyapunov Functional ◽  
Global Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Component System ◽  
Inhibitor Type ◽  
The One ◽  
Activator Inhibitor Type ◽  
Activator Inhibitor

This paper deals with a reaction-diffusion system with fractional reactions modeling -substances into interaction following activator-inhibitor's scheme. The existence of global solutions is obtained via a judicious Lyapunov functional that generalizes the one introduced by Masuda and Takahashi.

scholarly journals Global solution of reaction diffusion system with non diagonal matrix

2012 ◽  
Vol 45 (1) ◽  
Author(s):  
Abdelkader Moumeni ◽  
Lylia Salah Derradji
Keyword(s):  
Global Existence ◽  
Wide Class ◽  
Lyapunov Functional ◽  
Global Solutions ◽  
Reaction Diffusion ◽  
Functional Method ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Lyapunov Functional Method ◽  
Coupled Reaction

AbstractThe purpose of this paper is to prove the global existence in time of solutions for the coupled reaction-diffusion system:By combining the Lyapunov functional method with the regularizing effect, we show that global solutions exist. Our investigation applied for a wide class of the nonlinear terms

Stabilization of Dominant Structures in an Ionic Reaction-Diffusion System

1998 ◽  
Vol 63 (6) ◽  
pp. 761-769 ◽  
Author(s):  
Roland Krämer ◽  
Arno F. Münster
Keyword(s):  
Reaction Diffusion ◽  
Dominant Mode ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Perturbation ◽  
Dimensional System ◽  
One Dimensional ◽  
Brusselator Model ◽  
The One ◽  
Dominant Structure

We describe a method of stabilizing the dominant structure in a chaotic reaction-diffusion system, where the underlying nonlinear dynamics needs not to be known. The dominant mode is identified by the Karhunen-Loeve decomposition, also known as orthogonal decomposition. Using a ionic version of the Brusselator model in a spatially one-dimensional system, our control strategy is based on perturbations derived from the amplitude function of the dominant spatial mode. The perturbation is used in two different ways: A global perturbation is realized by forcing an electric current through the one-dimensional system, whereas the local perturbation is performed by modulating concentrations of the autocatalyst at the boundaries. Only the global method enhances the contribution of the dominant mode to the total fluctuation energy. On the other hand, the local method leads to simple bulk oscillation of the entire system.

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