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Existence and asymptotics of traveling waves for nonlocal diffusion systems

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  • Yu, Zhixian
  • Yuan, Rong

Abstract

In this paper, we deal with the existence and asymptotic behavior of traveling waves for nonlocal diffusion systems with delayed monostable reaction terms. We obtain the existence of traveling wave front by using upper-lower solutions method and Schauder’s fixed point theorem for c>c∗(τ) and using a limiting argument for c=c∗(τ). Moreover, we find a priori asymptotic behavior of traveling waves with the help of Ikehara’s Theorem by constructing a Laplace transform representation of a solution. Especially, the delay can slow the minimal wave speed for ∂2f(0,0)>0 and the delay is independent of the minimal wave speed for ∂2f(0,0)=0.

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  • Yu, Zhixian & Yuan, Rong, 2012. "Existence and asymptotics of traveling waves for nonlocal diffusion systems," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1361-1367.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:11:p:1361-1367
    DOI: 10.1016/j.chaos.2012.07.002
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    Cited by:

    1. Dongmei Yuan & Yuzhen Bai, 2019. "Stability of Traveling Wave Fronts for a Three Species Predator-Prey Model with Nonlocal Dispersals," Complexity, Hindawi, vol. 2019, pages 1-15, December.
    2. Wu, Weixin & Teng, Zhidong, 2021. "The periodic traveling waves in a diffusive periodic SIR epidemic model with nonlinear incidence," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

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