Spatiotemporal chaos arising from standing waves in a reaction-diffusion system with cross-diffusion

2012 ◽  
Vol 136 (3) ◽  
pp. 034903 ◽  
Author(s):  
Igal Berenstein ◽  
Carsten Beta
Keyword(s):  
Standing Waves ◽  
Reaction Diffusion ◽  
Spatiotemporal Chaos ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Cross Diffusion

Karhunen-Loève local characterization of spatiotemporal chaos in a reaction-diffusion system

2000 ◽  
Vol 61 (2) ◽  
pp. 1382-1385 ◽  
Author(s):  
Matthias Meixner ◽  
Scott M. Zoldi ◽  
Sumit Bose ◽  
Eckehard Schöll
Keyword(s):  
Reaction Diffusion ◽  
Spatiotemporal Chaos ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Local Characterization

Modulated Standing Waves in a Short Reaction−Diffusion System

1996 ◽  
Vol 100 (16) ◽  
pp. 6604-6607 ◽  
Author(s):  
Milos Dolnik ◽  
Anatol M. Zhabotinsky ◽  
Irving R. Epstein
Keyword(s):  
Standing Waves ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System

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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