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Research Article | Open Access

Traveling wavefront solutions in a nonlocal diffusion model with nonlocal delay effect

Dong Li1, Xuechun He1, Nengxing Tan2, Rong Zou3( )
School of Mathematics and Statistics, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
School of General Education, Chongqing Finance and Economics College, Chongqing 401320, China
School of Mathematics and Quantitative Economics, Guangxi University of Finance and Economics, Nanning 530003, China
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Abstract

This paper is devoted to investigating the existence of traveling wavefront solutions with a sufficiently large wave speed for a nonlocal diffusion model with nonlocal delay effect using a perturbation method. Our proof is based on an abstract formulation of the wave profile as a solution to an operator equation in a specific Banach space, combined with the Fredholm theory and the Banach contraction mapping principle. Several numerical simulations are presented to illustrate our main results.

Keywords

nonlocal diffusionnonlocal delaytraveling wavefront solutionperturbation method

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Electronic Research Archive
Volume 34 Issue 6,
May 2026
Pages 4172-4190
DOI: 10.3934/era.2026187

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Cite this article:
Li D, He X, Tan N, et al. Traveling wavefront solutions in a nonlocal diffusion model with nonlocal delay effect. Electronic Research Archive, 2026, 34(6): 4172-4190. https://doi.org/10.3934/era.2026187

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Received: 20 January 2026
Revised: 27 February 2026
Accepted: 14 April 2026
Published: 18 May 2026
©2026 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)