Electron. J. Differential Equations, Vol. 2022 (2022), No. 82, pp. 1-16.

Regular traveling waves for a reaction-diffusion equation with two nonlocal delays

Haiqin Zhao, Shi-Liang Wu

Abstract:
This article concerns regular traveling waves of a reaction-diffusion equation with two nonlocal delays arising from the study of a single species with immature and mature stages and different ages at reproduction. Establishing a necessary condition on the regular traveling waves, we prove the uniqueness of noncritical regular traveling waves, regardless of being monotone or not. Under a quasi-monotone assumption and among other things, we further show that all noncritical monotone traveling waves are exponentially stable, by establishing two comparison theorems and constructing an auxiliary lower equation.

Submitted August 26, 2022. Published December 12, 2022.
Math Subject Classifications: 35R10, 35B40, 92D30.
Key Words: Regular traveling fronts; reaction-diffusion equation; nonlocal delay; uniqueness; stability
DOI: https://doi.org/10.58997/ejde.2022.82

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Haiqin Zhao
School of Mathematics and Statistics
Xidian University
Xian, Shaanxi 710071, China
email: zhaohaiqin@xidian.edu.cn
Shi-Liang Wu
School of Mathematics and Statistics
Xidian University
Xian, Shaanxi 710071, China
email: slwu@xidian.edu.cn

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