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

Sheng Chen Fu; Je Chiang Tsai

doi:10.3934/dcds.2013.33.4041

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

Sheng Chen Fu^*, Je Chiang Tsai

^*Corresponding author for this work

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

Abstract

We consider the reaction-diffusion system ut = δu_xx - 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 language	English
Pages (from-to)	4041-4069
Number of pages	29
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	33
Issue number	9
DOIs	https://doi.org/10.3934/dcds.2013.33.4041
Publication status	Published - 2013 Sept
Externally published	Yes

Keywords

Acidic nitrateferroin reaction
Reaction-diffusion system
Stability
Travelling wave

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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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.",

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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

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JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

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

Abstract

Keywords

ASJC Scopus subject areas

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