Bang-Sheng Han, Meng-Xue Chang, Yinghui Yang
Abstract:
This article concerns a nonlocal bistable reaction-diffusion equation with an
integral term. By using Leray-Schauder degree theory, the shift functions and
Harnack inequality, we prove the existence of a traveling wave solution connecting
0 to an unknown positive steady state when the support of the integral
is not small. Furthermore, for a specific kernel function, the stability of positive
equilibrium is studied and some numerical simulations are given to show that the
unknown positive steady state may be a periodic steady state.
Finally, we demonstrate the periodic steady state indeed exists, using a
center manifold theorem.
Submitted October 31, 2019. Published July 30, 2020.
Math Subject Classifications: 35C07, 35B40, 35K57, 92D25.
Key Words: Reaction-diffusion equation; traveling waves; numerical simulation;
critical exponent.
DOI: 10.58997/ejde.2020.84
Show me the PDF file (1791 KB), TEX file for this article.
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Bang-Sheng Han School of Mathematics Southwest Jiaotong University Chengdu, Sichuan, 611756, China email: hanbangsheng@swjtu.edu.cn |
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Meng-Xue Chang School of Mathematics Southwest Jiaotong University Chengdu, Sichuan, 611756, China email: mengxue_chang@163.com |
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Yinghui Yang School of Mathematics Southwest Jiaotong University Chengdu, Sichuan, 611756, China email: yangyh8605@swjtu.edu.cn |
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