WEAK ENTIRE SOLUTIONS OF REACTION–INTERFACE SYSTEMS

Yan Yu Chen; Hirokazu Ninomiya; Chang Hong Wu

doi:10.3934/dcdsb.2022174

WEAK ENTIRE SOLUTIONS OF REACTION–INTERFACE SYSTEMS

Yan Yu Chen, Hirokazu Ninomiya^*, Chang Hong Wu

^*Corresponding author for this work

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, the singular limit problems arising from FitzHugh–Nagumo–type reaction–diffusion systems are studied, which are called reaction–interface systems. All weak entire solutions originating from finitely many excited intervals are completely characterized. For weak entire solutions originating from infinitely many excited intervals, periodic wave trains and time-periodic solutions are discussed. In particular, we study the dispersion relation of periodic wave trains and investigate the dependence of the propagation speed on the period.

Original language	English
Pages (from-to)	6015-6033
Number of pages	19
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	28
Issue number	12
DOIs	https://doi.org/10.3934/dcdsb.2022174
State	Published - Dec 2023

Keywords

Excitable system
back
free boundary problem
front
singular limit
traveling pulse solution

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abstract = "In this paper, the singular limit problems arising from FitzHugh–Nagumo–type reaction–diffusion systems are studied, which are called reaction–interface systems. All weak entire solutions originating from finitely many excited intervals are completely characterized. For weak entire solutions originating from infinitely many excited intervals, periodic wave trains and time-periodic solutions are discussed. In particular, we study the dispersion relation of periodic wave trains and investigate the dependence of the propagation speed on the period.",

keywords = "Excitable system, back, free boundary problem, front, singular limit, traveling pulse solution",

author = "Chen, {Yan Yu} and Hirokazu Ninomiya and Wu, {Chang Hong}",

year = "2023",

month = dec,

doi = "10.3934/dcdsb.2022174",

language = "English",

volume = "28",

pages = "6015--6033",

journal = "Discrete and Continuous Dynamical Systems - Series B",

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publisher = "American Institute of Mathematical Sciences",

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T1 - WEAK ENTIRE SOLUTIONS OF REACTION–INTERFACE SYSTEMS

AU - Chen, Yan Yu

AU - Ninomiya, Hirokazu

AU - Wu, Chang Hong

PY - 2023/12

Y1 - 2023/12

N2 - In this paper, the singular limit problems arising from FitzHugh–Nagumo–type reaction–diffusion systems are studied, which are called reaction–interface systems. All weak entire solutions originating from finitely many excited intervals are completely characterized. For weak entire solutions originating from infinitely many excited intervals, periodic wave trains and time-periodic solutions are discussed. In particular, we study the dispersion relation of periodic wave trains and investigate the dependence of the propagation speed on the period.

AB - In this paper, the singular limit problems arising from FitzHugh–Nagumo–type reaction–diffusion systems are studied, which are called reaction–interface systems. All weak entire solutions originating from finitely many excited intervals are completely characterized. For weak entire solutions originating from infinitely many excited intervals, periodic wave trains and time-periodic solutions are discussed. In particular, we study the dispersion relation of periodic wave trains and investigate the dependence of the propagation speed on the period.

KW - Excitable system

KW - back

KW - free boundary problem

KW - front

KW - singular limit

KW - traveling pulse solution

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U2 - 10.3934/dcdsb.2022174

DO - 10.3934/dcdsb.2022174

M3 - Article

AN - SCOPUS:85168377193

SN - 1531-3492

VL - 28

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JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 12

ER -

WEAK ENTIRE SOLUTIONS OF REACTION–INTERFACE SYSTEMS

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