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  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
Online ISSN 1552-4485; Print ISSN 0033-569X

Existence of traveling waves in a simple isothermal chemical system with the same order for autocatalysis and decay

Author: Je-Chiang Tsai
Journal: Quart. Appl. Math. 69 (2011), 123-146
MSC (2000): Primary 34A34, 34A12, 35K57
Published electronically: December 29, 2010
MathSciNet review: 2807981
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Abstract: The reaction-diffusion systems which are based on an isothermal autocatalytic chemical reaction involving both an autocatalytic step of the $ (m+1)$th order ( $ A+mB\rightarrow (m+1)B$) and a decay step of the same order ( $ B\rightarrow C$) have very rich and interesting dynamics. Previous studies in the literature indicate that traveling waves play a key role in understanding these interesting dynamical phenomena. However, there is a lack of rigorous proof of the existence of traveling waves to this system. Here we generalize this isothermal autocatalytic chemical reaction model and provide a rigorous proof of the existence of traveling waves for the resulting reaction-diffusion system which also includes the systems arising from epidemiology and the microbial growth in a flow reactor.

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Additional Information

Je-Chiang Tsai
Affiliation: Department of Mathematics, National Chung Cheng University, 168, University Road, Min-Hsiung, Chia-Yi 621, Taiwan

PII: S 0033-569X(2010)01236-7
Keywords: Isothermal autocatalytic chemical reaction, traveling waves, reaction-diffusion systems, centre manifold
Received by editor(s): July 29, 2009
Published electronically: December 29, 2010
Additional Notes: The author is supported in part by the National Science Council of Taiwan
Article copyright: © Copyright 2010 Brown University

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