Traveling wave solutions for nonlocal dispersal Fisher–KPP model with age structure

Tian, Xuan; Guo, Shangjiang

doi:10.1016/j.aml.2021.107593

Cited by 9 publications

(1 citation statement)

References 13 publications

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“…Such as [19] for a class of twospecies chemotaxis models with Lotka-Volterra competitive kinetics. In [35] for an age-structured nonlocal dispersal model derived from an epidemic model with vertical infection. In [37] for a class of nonlocal dispersal SIR epidemic models with nonlinear incidence.…”

Section: Introductionmentioning

confidence: 99%

Stability of Planar Traveling Waves for a Class of Lotka–Volterra Competition Systems with Time Delay and Nonlocal Reaction Term

Xue

Liu

2023

Qual. Theory Dyn. Syst.

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In this paper, we consider the multidimensional stability of planar traveling waves for a class of Lotka-Volterra competition systems with time delay and nonlocal reaction term in n-dimensional space. It is proved that, all planar traveling waves with speed c > c * are exponentially stable in the form of t − n 2 e −ϵτ σt , where constant σ > 0 and ϵ τ = ϵ(τ ) ∈ (0, 1) is a decreasing function for the time delay τ > 0. While, for the planar traveling waves with speed c = c * , we prove that they are algebraically stable in the form of t − n 2 . The Fourier transform plays a crucial role in transforming the competition systems to a linear delayed differential system. We establish the comparison principle and some estimates in weighted spaces L 1 w (R n ) and W 2,1 w (R n ) to obtain the main results.

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Section: Introductionmentioning

confidence: 99%

Stability of Planar Traveling Waves for a Class of Lotka–Volterra Competition Systems with Time Delay and Nonlocal Reaction Term

Xue

Liu

2023

Qual. Theory Dyn. Syst.

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Traveling waves of an epidemic model with general nonlinear incidence rate and infection-age structure

Tian

Guo

2022

Z. Angew. Math. Phys.

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Existence of periodic traveling waves in a nonlocal convection–diffusion model with chemotaxis and delay effect

Liu,

Guo

2023

Z. Angew. Math. Phys.

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We focus upon the existence of periodic traveling waves in a nonlocal reaction-diffusion model with chemotaxis and nonlocal delay effect. Based on the perturbation method, the existence of periodic traveling waves with large wave speed are obtained by the Lyapunov-Schmidt reduction and the implicit function theorem. The trick of the proof is to treat the wave profile as a solution of an operator in a suitable Banach space. Keywords nonlocal convection-diffusion model • chemotaxis • delay • periodic traveling waves • perturbation method Mathematics Subject Classification (2000) 35K57 • 34K05.

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Traveling wave solutions for nonlocal dispersal Fisher–KPP model with age structure

Cited by 9 publications

References 13 publications

Stability of Planar Traveling Waves for a Class of Lotka–Volterra Competition Systems with Time Delay and Nonlocal Reaction Term

Stability of Planar Traveling Waves for a Class of Lotka–Volterra Competition Systems with Time Delay and Nonlocal Reaction Term

Traveling waves of an epidemic model with general nonlinear incidence rate and infection-age structure

Existence of periodic traveling waves in a nonlocal convection–diffusion model with chemotaxis and delay effect

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