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.

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.

Location of Bifurcation Points for a Reaction-Diffusion System with Neumann-Signorini Conditions

2011 ◽  
Vol 11 (4) ◽  
Author(s):  
Jan Eisner ◽  
Martin Väth
Keyword(s):  
Space Dimension ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Neumann Condition ◽  
Dirichlet Conditions ◽  
Bifurcation Points ◽  
Signorini Condition ◽  
Activator Inhibitor ◽  
One Space Dimension

AbstractWe consider a reaction-diffusion system of activator-inhibitor or substrate-depletion type in one space dimension which is subject to diffusion-driven instability. We determine the change of bifurcation when a pure Neumann condition is supplemented with a Signorini condition. We show that this change differs essentially from the known case when also Dirichlet conditions are assumed.

scholarly journals Existence of Solutions for a Quasilinear Reaction Diffusion System

2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Canrong Tian
Keyword(s):  
Existence Of Solutions ◽  
Upper And Lower Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Reaction Functions ◽  
Engineering Problems ◽  
Activator Inhibitor

The degenerate reaction diffusion system has been applied to a variety of physical and engineering problems. This paper is extended the existence of solutions from the quasimonotone reaction functions (e.g., inhibitor-inhibitor mechanism) to the mixed quasimonotone reaction functions (e.g., activator-inhibitor mechanism). By Schauder fixed point theorem, it is shown that the system admits at least one positive solution if there exist a coupled of upper and lower solutions. This result is applied to a Lotka-Volterra predator-prey model.

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