Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



The existence of traveling wave fronts for a reaction-diffusion system modelling the acidic nitrate-ferroin reaction

Author: Sheng-Chen Fu
Journal: Quart. Appl. Math. 72 (2014), 649-664
MSC (2000): Primary 35K40; Secondary 34A34, 35Q80, 35K57
DOI: https://doi.org/10.1090/S0033-569X-2014-01349-5
Published electronically: October 28, 2014
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Abstract: We investigate the existence of traveling wave solutions to the one-dimensional reaction-diffusion system $ u_t=\delta u_{xx}-2uv/(\beta +u)$, $ v_t=v_{xx}+uv/(\beta +u)$, which describes the acidic nitrate-ferroin reaction. Here $ \beta $ is a positive constant, $ u$ and $ v$ represent the concentrations of the ferroin and acidic nitrate respectively, and $ \delta $ denotes the ratio of the diffusion rates. We show that this system has a unique, up to translation, traveling wave solution with speed $ c$ iff $ c\geq 2/\sqrt {\beta +1}$.

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Additional Information

Sheng-Chen Fu
Affiliation: Department of Mathematical Sciences, National Chengchi University, 64, S-2 Zhi-nan Road, Taipei 116, Taiwan
Email: fu@nccu.edu.tw

DOI: https://doi.org/10.1090/S0033-569X-2014-01349-5
Received by editor(s): August 22, 2012
Published electronically: October 28, 2014
Additional Notes: This work was partially supported by the National Science Council of the Republic of China under the contract 100-2115-M-004-003
Article copyright: © Copyright 2014 Brown University

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