Spatial dynamics of a nonlocal bistable reaction diffusion equation

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dc.contributor.authorHan, Bang-Sheng
dc.contributor.authorChang, Meng-Xue
dc.contributor.authorYang, Yinghui
dc.date.accessioned2021-10-04T16:21:53Z
dc.date.available2021-10-04T16:21:53Z
dc.date.issued2020-07-30
dc.description.abstractThis 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.departmentMathematics
dc.formatText
dc.format.extent23 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationHan, 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.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/14591
dc.language.isoen
dc.publisherTexas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 2020, San Marcos, Texas: Texas State University and University of North Texas.
dc.subjectReaction-diffusion equation
dc.subjectTraveling waves
dc.subjectNumerical simulation
dc.subjectCritical exponent
dc.titleSpatial dynamics of a nonlocal bistable reaction diffusion equationen_US
dc.typeArticle

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