Spatial dynamics of a nonlocal bistable reaction diffusion equation
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Date
2020-07-30
Authors
Han, Bang-Sheng
Chang, Meng-Xue
Yang, Yinghui
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
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.
Description
Keywords
Reaction-diffusion equation, Traveling waves, Numerical simulation, Critical exponent
Citation
Han, 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.
Rights
Attribution 4.0 International