scholarly journals A periodic reaction-diffusion model with a quiescent stage

2012 ◽  
Vol 17 (1) ◽  
pp. 283-295 ◽  
Author(s):  
Feng-Bin Wang ◽  
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Periodic Reaction ◽  
Quiescent Stage

scholarly journals Propagation dynamics of a nonlocal time-space periodic reaction-diffusion model with delay

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ning Wang ◽  
Zhi-Cheng Wang
Keyword(s):  
Diffusion Model ◽  
Critical Speed ◽  
Wave Speed ◽  
Upper And Lower Solutions ◽  
Reaction Diffusion ◽  
Linear Operators ◽  
Time Space ◽  
Reaction Diffusion Model ◽  
Periodic Reaction ◽  
Asymptotic Speed

<p style='text-indent:20px;'>This paper is concerned with a nonlocal time-space periodic reaction diffusion model with age structure. We first prove the existence and global attractivity of time-space periodic solution for the model. Next, by a family of principal eigenvalues associated with linear operators, we characterize the asymptotic speed of spread of the model in the monotone and non-monotone cases. Furthermore, we introduce a notion of transition semi-waves for the model, and then by constructing appropriate upper and lower solutions, and using the results of the asymptotic speed of spread, we show that transition semi-waves of the model in the non-monotone case exist when their wave speed is above a critical speed, and transition semi-waves do not exist anymore when their wave speed is less than the critical speed. It turns out that the asymptotic speed of spread coincides with the critical wave speed of transition semi-waves in the non-monotone case. In addition, we show that the obtained transition semi-waves are actually transition waves in the monotone case. Finally, numerical simulations for various cases are carried out to support our theoretical results.</p>

Asymptotic behaviour of a reaction–diffusion model with a quiescent stage

2007 ◽  
Vol 463 (2080) ◽  
pp. 1029-1043 ◽  
Author(s):  
Kate Fang Zhang ◽  
Xiao-Qiang Zhao
Keyword(s):  
Asymptotic Behaviour ◽  
Diffusion Model ◽  
Wave Speed ◽  
Global Attractivity ◽  
Travelling Waves ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Asymptotic Speed ◽  
Minimal Wave Speed ◽  
Quiescent Stage

This paper is devoted to the investigation of the asymptotic behaviour for a reaction–diffusion model with a quiescent stage. We first establish the existence of the asymptotic speed of spread and show that it coincides with the minimal wave speed for monotone travelling waves. Then we obtain a threshold result on the global attractivity of either zero or positive steady state in the case where the spatial domain is bounded.

scholarly journals A new analyzing technique for nonlinear time fractional Cauchy reaction-diffusion model equations

2020 ◽  
Vol 19 ◽  
pp. 103462 ◽  
Author(s):  
Hijaz Ahmad ◽  
Tufail A. Khan ◽  
Imtiaz Ahmad ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Model Equations
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