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

Author:

Fu Sheng-Chen

Abstract

We investigate the existence of traveling wave solutions to the one-dimensional reaction-diffusion system u t = δ u x x 2 u v / ( β + u ) u_t=\delta u_{xx}-2uv/(\beta +u) , v t = v x x + u v / ( β + u ) v_t=v_{xx}+uv/(\beta +u) , which describes the acidic nitrate-ferroin reaction. Here β \beta is a positive constant, u u and v v represent the concentrations of the ferroin and acidic nitrate respectively, and δ \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 c iff c 2 / β + 1 c\geq 2/\sqrt {\beta +1} .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics

Reference11 articles.

1. Lecture Notes in Biomathematics;Fife, Paul C.,1979

2. Quenching and propagation in KPP reaction-diffusion equations with a heat loss;Berestycki, Henri;Arch. Ration. Mech. Anal.,2005

3. R. J. Field and M. Burger, Oscillations and traveling waves in chemical systems, Wiley, New York, 1985.

4. Travelling waves of a reaction-diffusion model for the acidic nitrate-ferroin reaction;Fu, Sheng-Chen;Discrete Contin. Dyn. Syst. Ser. B,2011

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