Minimal lamellar structures in a periodic FitzHugh–Nagumo system. (May 2020)

• Record Type: Journal Article
• Authors: Acerbi, Emilio; Chen, Chao-Nien; Choi, Yung-Sze
• Is Part Of: Nonlinear analysis. Volume 194(2020)
• Publication Date: 2020-05
• Subjects: 49J40 -- 33C10 -- 92C15 -- 35K57; FitzHugh–Nagumo system -- Singular limit -- Nonlocal geometric variational problem -- Lamella; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.01.026
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: A singular limit of a FitzHugh–Nagumo system leads to a nonlocal geometric variational problem with periodic boundary conditions. We study the stationary lamellar set and give a criterion to select out the one with the lowest energy. Such an optimal structure is called a minimal lamella. While the empty set or the full torus is a global minimizer for appropriate parameter regimes, the minimal lamellae beat both in other circumstances. The concept of minimal lamella points out that a preferred 1D mesh size is universal.