Electron. J. Differential Equations, Vol. 2021 (2021), No. 54, pp. 1-22.

Propagating interface in reaction-diffusion equations with distributed delay

Haoyu Wang, Ge Tian

Abstract:
This article concerns the limiting behavior of the solution to a reaction-diffusion equation with distributed delay. We firstly consider the quasi-monotone situation and then investigate the non-monotone situation by constructing two auxiliary quasi-monotone equations. The limit behaviors of solutions of the equation can be obtained from the sandwich technique and the comparison principle of the Cauchy problem. It is proved that the propagation speed of the interface is equal to the minimum wave speed of the corresponding traveling waves. This makes possible to observe the minimum speed of traveling waves from a new perspective.

Submitted January 17, 2021. Published June 21, 2021.
Math Subject Classifications: 35B25, 35K57, 35C07, 35R35, 92D25.
Key Words: Reaction-diffusion equations; distributed delay; traveling wave; propagating interface.
DOI: https://doi.org/10.58997/ejde.2021.54

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Haoyu Wang
School of Information Science and Engineering
Lanzhou University
Lanzhou, Gansu,730000, China
email: wanghaoyu17@lzu.edu.cn
Ge Tian
School of Mathematics and Statistics
Lanzhou University
Lanzhou, Gansu 730000, China
email: tiang17@lzu.edu.cn

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