Electronic Journal of Differential Equations | |
Periodic traveling waves and asymptotic spreading of a monostable reaction-diffusion equations with nonlocal effects | |
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
【 预 览 】
Files | Size | Format | View |
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RO202307120000292ZK.pdf | 2002KB | download |