Skip to Main content Skip to Navigation
Journal articles

Multiple front standing waves in the FitzHugh-Nagumo equations

Abstract : There have been several existence results for the standing waves of FitzHugh-Nagumo equations. Such waves are the connecting orbits of an autonomous second-order Lagrangian system and the corresponding kinetic energy is an indefinite quadratic form in the velocity terms. When the system has two stable hyperbolic equilibria, there exist two stable standing fronts, which will be used in this paper as building blocks, to construct stable standing waves with multiple fronts in case the equilibria are of saddle-focus type. The idea to prove existence is somewhat close in spirit to [Buffoni-Sere, CPAM 49, 285-305]. However several differences are required in the argument: facing a strongly indefinite functional, we need to perform a nonlo-cal Lyapunov-Schmidt reduction; in order to justify the stability of multiple front standing waves, we rely on a more precise variational characterization of such critical points. Based on this approach, both stable and unstable standing waves are found.
Complete list of metadata

https://hal.archives-ouvertes.fr/hal-01758786
Contributor : Eric Séré Connect in order to contact the contributor
Submitted on : Friday, September 17, 2021 - 1:05:10 AM
Last modification on : Tuesday, January 18, 2022 - 3:24:13 PM

Files

multi-front_v3.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Chao-Nien Chen, Eric Séré. Multiple front standing waves in the FitzHugh-Nagumo equations. Journal of Differential Equations, Elsevier, 2021, 302, pp. 895-925. ⟨10.1016/j.jde.2021.08.005⟩. ⟨hal-01758786v3⟩

Share

Metrics

Les métriques sont temporairement indisponibles