School of Information Science and Engineering
Lanzhou University
Lanzhou, Gansu,730000, China
email: wanghaoyu17@lzu.edu.cn
School of Mathematics and Statistics
Lanzhou University
Lanzhou, Gansu 730000, China
email: tiang17@lzu.edu.cn
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
Show me the PDF file (393 KB), TEX file for this article.
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Haoyu Wang School of Information Science and Engineering Lanzhou University Lanzhou, Gansu,730000, China email: wanghaoyu17@lzu.edu.cn |
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Ge Tian School of Mathematics and Statistics Lanzhou University Lanzhou, Gansu 730000, China email: tiang17@lzu.edu.cn |
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