Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

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


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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Additional Information

Jong-Shenq Guo
Affiliation: Department of Mathematics, National Taiwan Normal University, 88, Section 4, Ting Chou Road, Taipei 116, Taiwan
Email: jsguo@math.ntnu.edu.tw

Je-Chiang Tsai
Affiliation: Department of Mathematics, National Chung Cheng University, 168, University Road, Min-Hsiung, Chia-Yi 621, Taiwan
Email: tsaijc@math.ccu.edu.tw

DOI: https://doi.org/10.1090/S0033-569X-09-01153-9
Keywords: Traveling waves, reaction-diffusion systems, centre manifold
Received by editor(s): March 13, 2008
Published electronically: May 6, 2009
Additional Notes: The first author was supported in part by the National Science Council of the Republic of China under the contracts NSC 96-2119-M-003-001.
The second author is the corresponding author and was partially supported by the National Science Council of the Republic of China under the contracts NSC 96-2115-M-194-003-MY3.
Article copyright: © Copyright 2009 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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