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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 35K40, 34A34, 35Q80, 35K57

Retrieve articles in all journals with MSC (2000): 35K40, 34A34, 35Q80, 35K57


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


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website