Spatial dynamics of a nonlocal bistable reaction diffusion equation
dc.contributor.author | Han, Bang-Sheng | |
dc.contributor.author | Chang, Meng-Xue | |
dc.contributor.author | Yang, Yinghui | |
dc.date.accessioned | 2021-10-04T16:21:53Z | |
dc.date.available | 2021-10-04T16:21:53Z | |
dc.date.issued | 2020-07-30 | |
dc.description.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. | |
dc.description.department | Mathematics | |
dc.format | Text | |
dc.format.extent | 23 pages | |
dc.format.medium | 1 file (.pdf) | |
dc.identifier.citation | Han, 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. | |
dc.identifier.issn | 1072-6691 | |
dc.identifier.uri | https://hdl.handle.net/10877/14591 | |
dc.language.iso | en | |
dc.publisher | Texas State University, Department of Mathematics | |
dc.rights | Attribution 4.0 International | |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
dc.source | Electronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas. | |
dc.subject | Reaction-diffusion equation | |
dc.subject | Traveling waves | |
dc.subject | Numerical simulation | |
dc.subject | Critical exponent | |
dc.title | Spatial dynamics of a nonlocal bistable reaction diffusion equation | |
dc.type | Article |