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Traveling waves in quadratic autocatalytic systems with complexing agent

  • * Corresponding author: Bogdan Kazmierczak

    * Corresponding author: Bogdan Kazmierczak

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

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  • 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).

    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 $

    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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