scholarly journals Approximate Controllability of a Reaction-Diffusion System with a Cross-Diffusion Matrix and Fractional Derivatives on Bounded Domains

2010 ◽  
Vol 2010 (1) ◽  
pp. 281238 ◽  
Author(s):  
Salah Badraoui
Keyword(s):  
Fractional Derivatives ◽  
Approximate Controllability ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Bounded Domains ◽  
Diffusion Matrix ◽  
Cross Diffusion

scholarly journals Necessary conditions for local and global existence to a reaction-diffusion system with fractional derivatives

2006 ◽  
Vol 2006 ◽  
pp. 1-8 ◽  
Author(s):  
Kamel Haouam ◽  
Mourad Sfaxi
Keyword(s):  
Global Existence ◽  
Fractional Derivatives ◽  
Necessary Conditions ◽  
Initial Conditions ◽  
Reaction Diffusion ◽  
Single Equation ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Existence Of A Solution

We give some necessary conditions for local and global existence of a solution to reaction-diffusion system of type (FDS) with temporal and spacial fractional derivatives. As in the case of single equation of type (STFE) studied by M. Kirane et al. (2005), we prove that these conditions depend on the behavior of initial conditions for large|x|.

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.

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