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The minimal propagation speed of travelling waves for autocatalytic reaction-diffusion equations

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Abstract

This paper proves the existence of travelling waves for autocatalytic reaction-diffusion systems of a non-diffusive reactant and a diffusive autocatalyst where quadratic and cubic autocatalyses occur concurrently with the ratio 1 :k. We give the estimate of the minimal speed of travelling waves which is consistent with the result obtaind by S. Focant and Th. Gallay for the systems where a reactant and an autocatalyst are both diffusive. We further discuss the value of the parameterk which assures the validity of the heuristic argument employed by J. Murray and others.

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Authors and Affiliations

  1. Department of Information and Communication Sciences, Kyoto Sangyo University, 603-8555, Kyoto, Japan

    Yuzo Hosono & Hirokazu Kawahara

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  1. Yuzo Hosono
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  2. Hirokazu Kawahara
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Hosono, Y., Kawahara, H. The minimal propagation speed of travelling waves for autocatalytic reaction-diffusion equations. Japan J. Indust. Appl. Math. 18, 445–458 (2001). https://doi.org/10.1007/BF03168585

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  • DOI: https://doi.org/10.1007/BF03168585

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