Traveling waves in quadratic autocatalytic systems with complexing agent

Wei-Chieh Chen; Bogdan Kazmierczak

doi:10.3934/dcdsb.2020364

Article Contents

2021, Volume 26, Issue 4: 1827-1842. Doi: 10.3934/dcdsb.2020364

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Traveling waves in quadratic autocatalytic systems with complexing agent

Wei-Chieh Chen^1, and
Bogdan Kazmierczak^2, ,

1.
Department of Applied Mathematics, National Chiao Tung University, No. 1001, Ta Hsueh Road, Hsinchu 300093, Taiwan
2.
Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw, Poland

^* Corresponding author: Bogdan Kazmierczak
^* Corresponding author: Bogdan Kazmierczak

Dedicated to Prof. Sze-Bi Hsu in appreciation of his inspiring ideas

Received: October 05, 2020

Revised: October 24, 2020

Early access: December 2020

Published: April 2021

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Abstract

The quadratic autocatalytic reaction forms a key step in a number of chemical reaction systems, and traveling waves are observed in such systems. In this study, we investigate the effect of complexation reactions on traveling waves in the quadratic autocatalytic reaction system. More precisely, under the assumption that the complexation reaction is fast relative to the autocatalytic reaction, we show that the governing system is reduced to a two-component reaction-diffusion system with density-dependent diffusivity. Further, the numerical evidence suggests that for some parameter values, a traveling wave solution of this reduced two-component system is nonlinearly selected. This is contrast to that associated with the quadratic autocatalytic reaction (without complexation reactions).

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Mathematics Subject Classification: 34A34, 34A12, 35K57.

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Figure 1. Time-evolution of the solution $ (A, B) $ of system (1.9) with $ L = 1600 $. The initial data is that $ A_0(x) = 1\; (0 \leq x \leq L) $, and $ B_0(x) = 0\; (20 \leq x \leq L) $ and $ 1\; (0 \leq x < 20) $. Here the parameters are $ d = 2, K = 2 $, and $ \sigma = 4 $

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Figure 2. The dependence of wave speed $ v_m $ on $ \sigma $. The parameter $ K = 2 $ and the diffusivity parameter $ d $ is $ 0.5 $, $ 1 $, $ 2 $ and $ 4 $ for panels (a), (b), (c) and (d), respectively

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References

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