Spiral Wave Solutions of Practical Reaction-Diffusion Systems

1980 ◽  
Vol 39 (1) ◽  
pp. 8-13 ◽  
Author(s):  
M. R. Duffy ◽  
N. F. Britton ◽  
J. D. Murray
Keyword(s):  
Spiral Wave ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Wave Solutions ◽  
Diffusion Systems

scholarly journals Traveling Wave Solutions for Epidemic Cholera Model with Disease-Related Death

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Tianran Zhang ◽  
Qingming Gou
Keyword(s):  
Laplace Transform ◽  
Traveling Wave ◽  
Upper And Lower Solutions ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Wave Solutions ◽  
Diffusion Systems ◽  
Prior Estimate ◽  
Minimal Wave Speed

Based on Codeço’s cholera model (2001), an epidemic cholera model that incorporates the pathogen diffusion and disease-related death is proposed. The formula for minimal wave speedc∗is given. To prove the existence of traveling wave solutions, an invariant cone is constructed by upper and lower solutions and Schauder’s fixed point theorem is applied. The nonexistence of traveling wave solutions is proved by two-sided Laplace transform. However, to apply two-sided Laplace transform, the prior estimate of exponential decrease of traveling wave solutions is needed. For this aim, a new method is proposed, which can be applied to reaction-diffusion systems consisting of more than three equations.

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