TRAVELING WAVEFRONTS OF A DELAYED LATTICE REACTION-DIFFUSION MODEL

Li Shu; Peixuan Weng; Yanling Tian

doi:10.11948/2015006

2015 Volume 5 Issue 1

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Li Shu, Peixuan Weng, Yanling Tian. TRAVELING WAVEFRONTS OF A DELAYED LATTICE REACTION-DIFFUSION MODEL[J]. Journal of Applied Analysis & Computation, 2015, 5(1): 64-76. doi: 10.11948/2015006

Citation:

Li Shu, Peixuan Weng, Yanling Tian. TRAVELING WAVEFRONTS OF A DELAYED LATTICE REACTION-DIFFUSION MODEL[J]. Journal of Applied Analysis & Computation, 2015, 5(1): 64-76. doi: 10.11948/2015006

TRAVELING WAVEFRONTS OF A DELAYED LATTICE REACTION-DIFFUSION MODEL

School of Mathematics, South China Normal University, 510631 Guangzhou, P. R. China

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Abstract

Abstract

We investigate a system of delayed lattice differential system which is a model of pioneer-climax species distributed on one dimensional discrete space. We show that there exists a constant c^∗>0, such that the model has traveling wave solutions connecting a boundary equilibrium to a co-existence equilibrium for c ≥ c^∗. We also argue that c^∗ is the minimal wave speed and the delay is harmless. The Schauder's fixed point theorem combining with upper-lower solution technique is used for showing the existence of wave solution.
- Pioneer-climax model /
- lattice differential system /
- harmless delay /
- traveling wave solution /
- minimal wave speed
MSC: 34K25;45J05;92D25

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References

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