Spatial dynamics of a nonlocal bistable reaction diffusion equation
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This 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.
CitationHan, B. S., Chang, M. X., & Yang, Y. (2020). Spatial dynamics of a nonlocal bistable reaction diffusion equation. Electronic Journal of Differential Equations, 2020(84), pp. 1-23.
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