Taiwanese Journal of Mathematics

Localized Front Structures in FitzHugh-Nagumo Equations

Chao-Nien Chen, Che-Hao Lin, and Shyuh-yaur Tzeng

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Abstract

We are interested in various types of localized waves in FitzHugh-Nagumo equations. Variational methods have been successfully worked out to establish the existence of traveling and standing waves. Starting with a simple planar traveling front, an ordered method is employed to demonstrate different front propagation between two stable equilibria. If these two stable equilibria are in the same energy level, a saddle-focus condition ensures that there are infinite number of standing waves with multiple fronts.

Article information

Source
Taiwanese J. Math., Volume 23, Number 2 (2019), 333-349.

Dates
Received: 26 April 2018
Revised: 5 November 2018
Accepted: 22 November 2018
First available in Project Euclid: 6 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1544086877

Digital Object Identifier
doi:10.11650/tjm/181112

Mathematical Reviews number (MathSciNet)
MR3936003

Subjects
Primary: 34C37: Homoclinic and heteroclinic solutions 35J50: Variational methods for elliptic systems 35K57: Reaction-diffusion equations

Keywords
FitzHugh-Nagumo equations traveling front solution localized structure wave propagation

Citation

Chen, Chao-Nien; Lin, Che-Hao; Tzeng, Shyuh-yaur. Localized Front Structures in FitzHugh-Nagumo Equations. Taiwanese J. Math. 23 (2019), no. 2, 333--349. doi:10.11650/tjm/181112. https://projecteuclid.org/euclid.twjm/1544086877


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