scholarly journals Minimal wave speed for a class of non-cooperative reaction–diffusion systems of three equations

2017 ◽  
Vol 262 (9) ◽  
pp. 4724-4770 ◽  
Author(s):  
Tianran Zhang
Keyword(s):  
Wave Speed ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Minimal Wave Speed

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.

scholarly journals Periodic traveling fronts for partially degenerate reaction-diffusion systems with bistable and time-periodic nonlinearity

2019 ◽  
Vol 9 (1) ◽  
pp. 923-957
Author(s):  
Shi-Liang Wu ◽  
Cheng-Hsiung Hsu
Keyword(s):  
Periodic Solutions ◽  
Wave Speed ◽  
Reaction Diffusion ◽  
Wave Speeds ◽  
Reaction Diffusion Systems ◽  
Liapunov Stability ◽  
Traveling Fronts ◽  
Diffusion Systems ◽  
Stable Periodic ◽  
Time Periodic

Abstract This paper is concerned with the periodic traveling fronts for partially degenerate reaction-diffusion systems with bistable and time-periodic nonlinearity. We first determine the signs of wave speeds for two monostable periodic traveling fronts of the system. Then, we prove the existence of periodic traveling fronts connecting two stable periodic solutions. An estimate of the wave speed is also obtained. Further, we prove the monotonicity, uniqueness (up to a translation), Liapunov stability and exponentially asymptotical stability of the smooth bistable periodic traveling fronts.

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