scholarly journals Traveling wave fronts of delayed non-local diffusion systems without quasimonotonicity

2008 ◽  
Vol 346 (2) ◽  
pp. 415-424 ◽  
Author(s):  
Shuxia Pan
Keyword(s):  
Traveling Wave ◽  
Wave Fronts ◽  
Traveling Wave Fronts ◽  
Diffusion Systems ◽  
Non Local ◽  
Local Diffusion

scholarly journals Some Qualitative Properties of Traveling Wave Fronts of Nonlocal Diffusive Competition-Cooperation Systems of Three Species with Delays

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-19
Author(s):  
Meiping Yao ◽  
Pengzhi Qiao ◽  
Yang Wang
Keyword(s):  
Asymptotic Behavior ◽  
Traveling Wave ◽  
Nonlocal Diffusion ◽  
Strict Monotonicity ◽  
Qualitative Properties ◽  
Wave Fronts ◽  
Traveling Wave Fronts ◽  
Sliding Method ◽  
Diffusion Systems ◽  
Stable Manifold Theorem

This paper is concerned with nonlocal diffusion systems of three species with delays. By modified version of Ikehara’s theorem, we prove that the traveling wave fronts of such system decay exponentially at negative infinity, and one component of such solutions also decays exponentially at positive infinity. In order to obtain more information of the asymptotic behavior of such solutions at positive infinity, for the special kernels, we discuss the asymptotic behavior of such solutions of such system without delays, via the stable manifold theorem. In addition, by using the sliding method, the strict monotonicity and uniqueness of traveling wave fronts are also obtained.

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