Zhi-Jiao Yang, Guo-Bao Zhang, Juan He
Abstract:
This article concerns the traveling wavefronts of a discrete diffusive
Lotka-Volterra competition system with nonlocal nonlinearities.
We first prove that there exists a \(c_*>0\) such that when the wave speed
is large than or equals to \(c_*\), the system admits an increasing
traveling wavefront connecting two boundary equilibria by the upper-lower
solutions method. Furthermore, we prove that
(i) all traveling wavefronts with speed \(c>c^{*}(>c_*)\) are globally
stable with exponential convergence rate
\(t^{-1/2}e^{-\varepsilon_{\tau}\sigma t}\),
where \(\sigma>0\) and \(\varepsilon_{\tau}=\varepsilon(\tau)\in (0,1)\)
is a decreasing function for the time delay \(\tau>0\);
(ii) the traveling wavefronts with speed \(c=c^{*}\) are globally
algebraically stable in the algebraic form \(t^{-1/2}\).
The approaches are the weighted energy method, the comparison
principle and Fourier transform.
Submitted July 23, 2024. Published January 4, 2025.
Math Subject Classifications: 35K55, 35C07, 92D25.
Key Words: Epidemic system; nonlocal dispersal; bistable traveling waves; stability; time delay.
DOI: 10.58997/ejde.2025.02
Show me the PDF file (424 KB), TEX file for this article.
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Zhi-Jiao Yang College of Mathematics and Statistics Northwest Normal University Lanzhou, Gansu 730070, China email: 1493801034@qq.com |
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Guo-Bao Zhang College of Mathematics and Statistics Northwest Normal University Lanzhou, Gansu 730070, China email: zhanggb2011@nwnu.edu.cn |
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Juan He College of Mathematics and Statistics Northwest Normal University Lanzhou, Gansu 730070, China email: 1099912126@qq.com |
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