scholarly journals Numerical Approximation to Nonlinear One Dimensional Coupled Reaction Diffusion System

2017 ◽  
Vol 05 (08) ◽  
pp. 1551-1574 ◽  
Author(s):  
Shahid Hasnain ◽  
Daoud Suleiman Mashat ◽  
Muhammad Saqib ◽  
Shafeek A. Ghaleb ◽  
Noorah Y. Mshary
Keyword(s):  
Numerical Approximation ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
One Dimensional ◽  
Coupled Reaction

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.

Dynamics of a coupled reaction-diffusion system

1990 ◽  
Vol 42 (1) ◽  
pp. 81-84 ◽  
Author(s):  
B Etlicher ◽  
H Wilhelmsson
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Coupled Reaction

Unique continuation for a reaction-diffusion system with cross diffusion

2019 ◽  
Vol 27 (4) ◽  
pp. 511-525 ◽  
Author(s):  
Bin Wu ◽  
Ying Gao ◽  
Zewen Wang ◽  
Qun Chen
Keyword(s):  
Unique Continuation ◽  
Reaction Diffusion ◽  
Cauchy Data ◽  
Carleman Estimate ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Lateral Boundary ◽  
Strongly Coupled ◽  
Cross Diffusion ◽  
Coupled Reaction

Abstract This paper concerns unique continuation for a reaction-diffusion system with cross diffusion, which is a drug war reaction-diffusion system describing a simple dynamic model of a drug epidemic in an idealized community. We first establish a Carleman estimate for this strongly coupled reaction-diffusion system. Then we apply the Carleman estimate to prove the unique continuation, which means that the Cauchy data on any lateral boundary determine the solution uniquely in the whole domain.

scholarly journals Numerical approximation of a reaction-diffusion system with fast reversible reaction

2010 ◽  
Vol 31 (5) ◽  
pp. 631-654 ◽  
Author(s):  
Robert Eymard ◽  
Danielle Hilhorst ◽  
Hideki Murakawa ◽  
Michal Olech
Keyword(s):  
Numerical Approximation ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Reversible Reaction
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