Electron. J. Differential Equations, Vol. 2021 (2021), No. 22, pp. 124.
Periodic traveling waves and asymptotic spreading of a monostable
reactiondiffusion equations with nonlocal effects
BangSheng Han, DeYu Kong, Qihong Shi, Fan Wang
Abstract:
This article concerns the dynamical behavior for a reactiondiffusion equation with
integral term. First, by using bifurcation analysis and center manifold theorem,
the existence of periodic steadystate 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: Reactiondiffusion; nonlocal delay; periodic traveling wave;
asymptotic behavior; numerical simulation, critical exponent.
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BangSheng Han
School of Mathematics
Southwest Jiaotong University
Chengdu, Sichuan 611756, China
email: hanbangsheng@swjtu.edu.cn


DeYu Kong
School of Mathematics
Southwest Jiaotong University
Chengdu, Sichuan 611756, China
email: KongDY@my.swjtu.edu.cn


Qihong Shi
Department of Mathematics
Lanzhou University of Technology
Lanzhou, Gansu 730000, China
email: shiqh@lut.edu.cn


Fan Wang
School of Mathematics
Southwest Jiaotong University
Chengdu, Sichuan 611756, China
email: wangf767@swjtu.edu.cn

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