Quarterly of Applied Mathematics

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

Author(s): Jong-Shenq Guo; Je-Chiang Tsai
Journal: Quart. Appl. Math. 67 (2009), 559-578.
MSC (2000): Primary 34A34, 34A12; Secondary 35K57
Posted: May 6, 2009
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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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Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 34A34, 34A12, 35K57

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

PII: S0033-569X-09-01153-9
Keywords: Traveling waves, reaction-diffusion systems, centre manifold
Received by editor(s): March 13, 2008
Posted: 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.
Copyright of article: Copyright 2009, Brown University
The copyright for this article reverts to public domain after 28 years from publication.

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