Han, Bang-ShengChang, Meng-XueYang, Yinghui2021-10-042021-10-042020-07-30Han, B. S., Chang, M. X., & Yang, Y. (2020). Spatial dynamics of a nonlocal bistable reaction diffusion equation. <i>Electronic Journal of Differential Equations, 2020</i>(84), pp. 1-23.1072-6691https://hdl.handle.net/10877/14591This article concerns a nonlocal bistable reaction-diffusion equation with an integral term. By using Leray-Schauder degree theory, the shift functions and Harnack inequality, we prove the existence of a traveling wave solution connecting 0 to an unknown positive steady state when the support of the integral is not small. Furthermore, for a specific kernel function, the stability of positive equilibrium is studied and some numerical simulations are given to show that the unknown positive steady state may be a periodic steady state. Finally, we demonstrate the periodic steady state indeed exists, using a center manifold theorem.Text23 pages1 file (.pdf)enAttribution 4.0 InternationalReaction-diffusion equationTraveling wavesNumerical simulationCritical exponentArticle