Cross-diffusion influence on the non-linear L2-stability analysis for a Lotka Volterra reaction diffusion system of PDEs

2007 ◽  
Vol 72 (5) ◽  
pp. 540-555 ◽  
Author(s):  
J. N. Flavin ◽  
S. Rionero
Keyword(s):  
Stability Analysis ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Cross Diffusion ◽  
Non Linear ◽  
L2 Stability

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.

Non-linear dynamics of a self-igniting reaction–diffusion system

2000 ◽  
Vol 55 (2) ◽  
pp. 303-309 ◽  
Author(s):  
G Continillo ◽  
V Faraoni ◽  
P.L Maffettone ◽  
S Crescitelli
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Linear Dynamics ◽  
Non Linear

Mathematical and computational studies of fractional reaction-diffusion system modelling predator-prey interactions

2018 ◽  
Vol 0 (0) ◽  
Author(s):  
Kolade M. Owolabi ◽  
Edson Pindza
Keyword(s):  
Stability Analysis ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
System Modelling ◽  
Computational Studies ◽  
Mathematical Basis ◽  
Transform Method ◽  
Reaction Diffusion Systems ◽  
Fractional Reaction

Abstract This paper provides the essential mathematical basis for computational studies of space fractional reaction-diffusion systems, from biological and numerical analysis perspectives. We adopt linear stability analysis to derive conditions on the choice of parameters that lead to biologically meaningful equilibria. The stability analysis has a lot of implications for understanding the various spatiotemporal and chaotic behaviors of the species in the spatial domain. For the solution of the full reaction-diffusion system modelled by the fractional partial differential equations, we introduced the Fourier transform method to discretize in space and advance the resulting system of ordinary differential equation in time with the fourth-order exponential time differencing scheme. Numerical results.

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