Periodic traveling waves and asymptotic spreading of a monostable reaction-diffusion equations with nonlocal effects

Electronic Journal of Differential Equations

article

Bang-Sheng Han¹  De-Yu Kong¹  Qihong Shi²  Fan Wang¹ 

[1] School of Mathematics Southwest Jiaotong University Chengdu;Department of Mathematics Lanzhou University of Technology Lanzhou

关键词: Reaction-diffusion;    nonlocal delay;    periodic traveling wave;    asymptotic behavior;    numerical simulation;    critical exponent.;   

DOI  :  10.58997/ejde.2021.22

学科分类：数学（综合）

来源: Texas State University

【 摘 要 】

This article concerns the dynamical behavior for a reaction-diffusion equation withintegral term. First, by using bifurcation analysis and center manifold theorem,the existence of periodic steady-state solution are established for a special kernelfunction and a general kernel function respectively.Then, we prove the model admits periodic traveling wave solutions connecting thisperiodic steady state to the uniform steady state u=1 by applying center manifoldreduction and the analysis to phase diagram. By numerical simulations, we also showthe 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 compactsupport is investigated.

【 授权许可】

CC BY