Stability of travelling waves of a reaction-diffusion system for the acidic nitrate-ferroin reaction

Sheng Chen Fu, Je-Chiang Tsai

Research output: Contribution to journalArticle

Abstract

We consider the reaction-diffusion system ut = δuxx - 2uv/(β+u), vt = vxx +uv /(β+u), which is used to model the acidic nitrate-ferroin reaction. Here β is a positive constant, u and v represent the concentrations of the ferroin and acidic nitrate respectively, and δ denotes the ratio of the diffusion rates. The existence of travelling waves for this system is known. Using energy functionals, we provide a stability analysis of travelling waves.

Original languageEnglish
Pages (from-to)4041-4069
Number of pages29
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume33
Issue number9
DOIs
Publication statusPublished - 2013 Sep 1

Fingerprint

Nitrate
Reaction-diffusion System
Traveling Wave
Nitrates
Stability Analysis
Denote
Energy
Model

Keywords

  • Acidic nitrateferroin reaction
  • Reaction-diffusion system
  • Stability
  • Travelling wave

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics
  • Analysis

Cite this

Stability of travelling waves of a reaction-diffusion system for the acidic nitrate-ferroin reaction. / Fu, Sheng Chen; Tsai, Je-Chiang.

In: Discrete and Continuous Dynamical Systems- Series A, Vol. 33, No. 9, 01.09.2013, p. 4041-4069.

Research output: Contribution to journalArticle

@article{38ac5d10ef3b4593a752b4c71a38afe8,
title = "Stability of travelling waves of a reaction-diffusion system for the acidic nitrate-ferroin reaction",
abstract = "We consider the reaction-diffusion system ut = δuxx - 2uv/(β+u), vt = vxx +uv /(β+u), which is used to model the acidic nitrate-ferroin reaction. Here β is a positive constant, u and v represent the concentrations of the ferroin and acidic nitrate respectively, and δ denotes the ratio of the diffusion rates. The existence of travelling waves for this system is known. Using energy functionals, we provide a stability analysis of travelling waves.",
keywords = "Acidic nitrateferroin reaction, Reaction-diffusion system, Stability, Travelling wave",
author = "Fu, {Sheng Chen} and Je-Chiang Tsai",
year = "2013",
month = "9",
day = "1",
doi = "10.3934/dcds.2013.33.4041",
language = "English",
volume = "33",
pages = "4041--4069",
journal = "Discrete and Continuous Dynamical Systems",
issn = "1078-0947",
publisher = "Southwest Missouri State University",
number = "9",

}

TY - JOUR

T1 - Stability of travelling waves of a reaction-diffusion system for the acidic nitrate-ferroin reaction

AU - Fu, Sheng Chen

AU - Tsai, Je-Chiang

PY - 2013/9/1

Y1 - 2013/9/1

N2 - We consider the reaction-diffusion system ut = δuxx - 2uv/(β+u), vt = vxx +uv /(β+u), which is used to model the acidic nitrate-ferroin reaction. Here β is a positive constant, u and v represent the concentrations of the ferroin and acidic nitrate respectively, and δ denotes the ratio of the diffusion rates. The existence of travelling waves for this system is known. Using energy functionals, we provide a stability analysis of travelling waves.

AB - We consider the reaction-diffusion system ut = δuxx - 2uv/(β+u), vt = vxx +uv /(β+u), which is used to model the acidic nitrate-ferroin reaction. Here β is a positive constant, u and v represent the concentrations of the ferroin and acidic nitrate respectively, and δ denotes the ratio of the diffusion rates. The existence of travelling waves for this system is known. Using energy functionals, we provide a stability analysis of travelling waves.

KW - Acidic nitrateferroin reaction

KW - Reaction-diffusion system

KW - Stability

KW - Travelling wave

UR - http://www.scopus.com/inward/record.url?scp=84876046127&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84876046127&partnerID=8YFLogxK

U2 - 10.3934/dcds.2013.33.4041

DO - 10.3934/dcds.2013.33.4041

M3 - Article

AN - SCOPUS:84876046127

VL - 33

SP - 4041

EP - 4069

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 9

ER -