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

[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.

[学科分类] 数学（综合）

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