Traveling waves in nonlocal diffusion systems with delays and partial quasi-monotonicity

2011 ◽  
Vol 26 (4) ◽  
pp. 464-482 ◽  
Author(s):  
Zhao-quan Xu ◽  
Pei-xuan Weng
Keyword(s):  
Traveling Waves ◽  
Nonlocal Diffusion ◽  
Diffusion Systems

scholarly journals Non-cooperative Fisher–KPP systems: Asymptotic behavior of traveling waves

2018 ◽  
Vol 28 (06) ◽  
pp. 1067-1104 ◽  
Author(s):  
Léo Girardin
Keyword(s):  
Traveling Waves ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Positive Cone ◽  
Precise Description ◽  
Kpp Equation ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Null State

This paper is concerned with non-cooperative parabolic reaction–diffusion systems which share structural similarities with the scalar Fisher–KPP equation. In a previous paper, we established that these systems admit traveling wave solutions whose profiles connect the null state to a compact subset of the positive cone. The main object of this paper is the investigation of a more precise description of these profiles. Non-cooperative KPP systems can model various phenomena where the following three mechanisms occur: local diffusion in space, linear cooperation and superlinear competition.

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