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

This article concerns the dynamical behavior for a reaction-diffusion equation with integral term. First, by using bifurcation analysis and center manifold theorem, existence of periodic steady-state solution are established special kernel function general respectively. Then, we prove model admits traveling wave solutions connecting this steady state to uniform u=1 applying reduction phase diagram. By numerical simulations, also show change profile as coefficient aggregate term increases. Also, introducing truncation function, shift some auxiliary functions, asymptotic Cauchy problem initial having compact support is investigated.
 For more information see https://ejde.math.txstate.edu/Volumes/2021/22/abstr.html