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.

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 Method Using Cubic B-Spline for a Strongly Coupled Reaction-Diffusion System

PLoS ONE ◽  
2014 ◽  
Vol 9 (1) ◽  
pp. e83265 ◽  
Author(s):  
Muhammad Abbas ◽  
Ahmad Abd. Majid ◽  
Ahmad Izani Md. Ismail ◽  
Abdur Rashid
Keyword(s):  
Numerical Method ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Strongly Coupled ◽  
B Spline ◽  
Coupled Reaction

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

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
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