Traveling waves of two-component reaction-diffusion systems arising from higher order autocatalytic models

Jong Shenq Guo; Je Chiang Tsai

doi:10.1090/S0033-569X-09-01153-9

Traveling waves of two-component reaction-diffusion systems arising from higher order autocatalytic models

Jong Shenq Guo^*, Je Chiang Tsai

^*Corresponding author for this work

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

10 Citations (Scopus)

Abstract

We study the existence and uniqueness of traveling wave solutions for a class of two-component reaction-diffusion systems with one species being immobile. Such a system has a variety of applications in epidemiology, bio-reactor models, and isothermal autocatalytic chemical reaction systems. Our result not only generalizes earlier results of Ai and Huang (Proceedings of the Royal Society of Edinburgh 2005; 135A:663-675), but also establishes the existence and uniqueness of traveling wave solutions to the reactiondiffusion system for an isothermal autocatalytic chemical reaction of any order in which the autocatalyst is assumed to decay to the inert product at a rate of the same order.

Original language	English
Pages (from-to)	559-578
Number of pages	20
Journal	Quarterly of Applied Mathematics
Volume	67
Issue number	3
DOIs	https://doi.org/10.1090/S0033-569X-09-01153-9
Publication status	Published - 2009
Externally published	Yes

Keywords

Centre manifold
Reaction-diffusion systems
Traveling waves

ASJC Scopus subject areas

Applied Mathematics

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10.1090/S0033-569X-09-01153-9

Cite this

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abstract = "We study the existence and uniqueness of traveling wave solutions for a class of two-component reaction-diffusion systems with one species being immobile. Such a system has a variety of applications in epidemiology, bio-reactor models, and isothermal autocatalytic chemical reaction systems. Our result not only generalizes earlier results of Ai and Huang (Proceedings of the Royal Society of Edinburgh 2005; 135A:663-675), but also establishes the existence and uniqueness of traveling wave solutions to the reactiondiffusion system for an isothermal autocatalytic chemical reaction of any order in which the autocatalyst is assumed to decay to the inert product at a rate of the same order.",

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AU - Guo, Jong Shenq

AU - Tsai, Je Chiang

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N2 - We study the existence and uniqueness of traveling wave solutions for a class of two-component reaction-diffusion systems with one species being immobile. Such a system has a variety of applications in epidemiology, bio-reactor models, and isothermal autocatalytic chemical reaction systems. Our result not only generalizes earlier results of Ai and Huang (Proceedings of the Royal Society of Edinburgh 2005; 135A:663-675), but also establishes the existence and uniqueness of traveling wave solutions to the reactiondiffusion system for an isothermal autocatalytic chemical reaction of any order in which the autocatalyst is assumed to decay to the inert product at a rate of the same order.

AB - We study the existence and uniqueness of traveling wave solutions for a class of two-component reaction-diffusion systems with one species being immobile. Such a system has a variety of applications in epidemiology, bio-reactor models, and isothermal autocatalytic chemical reaction systems. Our result not only generalizes earlier results of Ai and Huang (Proceedings of the Royal Society of Edinburgh 2005; 135A:663-675), but also establishes the existence and uniqueness of traveling wave solutions to the reactiondiffusion system for an isothermal autocatalytic chemical reaction of any order in which the autocatalyst is assumed to decay to the inert product at a rate of the same order.

KW - Centre manifold

KW - Reaction-diffusion systems

KW - Traveling waves

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Traveling waves of two-component reaction-diffusion systems arising from higher order autocatalytic models

Abstract

Keywords

ASJC Scopus subject areas

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