A second-order linearized difference scheme for a strongly coupled reaction-diffusion system

2007 ◽  
Vol 24 (1) ◽  
pp. 9-23 ◽  
Author(s):  
Hai-Yan Cao ◽  
Zhi-Zhong Sun
Keyword(s):  
Difference Scheme ◽  
Reaction Diffusion ◽  
Second Order ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Strongly Coupled ◽  
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 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 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.

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

On a reaction–diffusion system modelling infectious diseases without lifetime immunity

2021 ◽  
pp. 1-25
Author(s):  
HONG-MING YIN
Keyword(s):  
Diffusion Coefficients ◽  
A Priori ◽  
Main Tool ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Sobolev Embedding ◽  
System Modelling ◽  
Strongly Coupled ◽  
Elliptic And Parabolic Equations

In this paper, we study a mathematical model for an infectious disease caused by a virus such as Cholera without lifetime immunity. Due to the different mobility for susceptible, infected human and recovered human hosts, the diffusion coefficients are assumed to be different. The resulting system is governed by a strongly coupled reaction–diffusion system with different diffusion coefficients. Global existence and uniqueness are established under certain assumptions on known data. Moreover, global asymptotic behaviour of the solution is obtained when some parameters satisfy certain conditions. These results extend the existing results in the literature. The main tool used in this paper comes from the delicate theory of elliptic and parabolic equations. Moreover, the energy method and Sobolev embedding are used in deriving a priori estimates. The analysis developed in this paper can be employed to study other epidemic models in biological, ecological and health sciences.

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