Wavefronts for a non-local reaction-diffusion population model with general distributive maturity

2008 ◽  
Vol 73 (3) ◽  
pp. 477-495 ◽  
Author(s):  
P. Weng ◽  
J. Wu
Keyword(s):  
Population Model ◽  
Local Reaction ◽  
Reaction Diffusion ◽  
Non Local

scholarly journals Traveling Waves Solutions for Delayed Temporally Discrete Non-Local Reaction-Diffusion Equation

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1999
Author(s):  
Hongpeng Guo ◽  
Zhiming Guo
Keyword(s):  
Diffusion Equation ◽  
Traveling Wave ◽  
Local Reaction ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Birth Function ◽  
Wave Solutions ◽  
Monotonicity Assumption ◽  
Non Local

This paper deals with the existence of traveling wave solutions to a delayed temporally discrete non-local reaction diffusion equation model, which has been derived recently for a single species with age structure. When the birth function satisfies monotonic condition, we obtained the traveling wavefront by using upper and lower solution methods together with monotonic iteration techniques. Otherwise, without the monotonicity assumption for birth function, we constructed two auxiliary equations. By means of the traveling wavefronts of the auxiliary equations, using the Schauder’ fixed point theorem, we proved the existence of a traveling wave solution to the equation under consideration with speed c>c*, where c*>0 is some constant. We found that the delayed temporally discrete non-local reaction diffusion equation possesses the dynamical consistency with its time continuous counterpart at least in the sense of the existence of traveling wave solutions.

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