Bang-Sheng Han, De-Yu Kong, Qihong Shi, Fan Wang
Abstract:
This article concerns the dynamical behavior for a reaction-diffusion equation with
integral term. First, by using bifurcation analysis and center manifold theorem,
the existence of periodic steady-state solution are established for a special kernel
function and a general kernel function respectively.
Then, we prove the model admits periodic traveling wave solutions connecting this
periodic steady state to the uniform steady state u=1 by applying center manifold
reduction and the analysis to phase diagram. By numerical simulations, we also show
the change of the wave profile as the coefficient of aggregate term increases.
Also, by introducing a truncation function, a shift function and some auxiliary functions,
the asymptotic behavior for the Cauchy problem with initial function having compact
support is investigated.
Submitted August 27, 2020. Published March 30, 2021.
Math Subject Classifications: 35C07, 35B10, 35B40, 35R09, 92D25.
Key Words: Reaction-diffusion; nonlocal delay; periodic traveling wave;
asymptotic behavior; numerical simulation, critical exponent.
Show me the PDF file (2050 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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De-Yu Kong School of Mathematics Southwest Jiaotong University Chengdu, Sichuan 611756, China email: KongDY@my.swjtu.edu.cn |
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Qihong Shi Department of Mathematics Lanzhou University of Technology Lanzhou, Gansu 730000, China email: shiqh@lut.edu.cn |
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Fan Wang School of Mathematics Southwest Jiaotong University Chengdu, Sichuan 611756, China email: wangf767@swjtu.edu.cn |
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