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

Guo, Jong-Shenq; Tsai, Je-Chiang

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

Authors: Jong-Shenq Guo and Je-Chiang Tsai
Journal: Quart. Appl. Math. 67 (2009), 559-578
MSC (2000): Primary 34A34, 34A12; Secondary 35K57
DOI: https://doi.org/10.1090/S0033-569X-09-01153-9
Published electronically: May 6, 2009
MathSciNet review: 2547640
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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 reaction-diffusion 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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