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Traveling wave speed and solution in reaction-diffusion equation in one dimension

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Abstract

By Painlevé analysis, traveling wave speed and solution of reaction-diffusion equations for the concentration of one species in one spatial dimension are in detail investigated. When the exponent of the creation term is larger than the one of the annihilation term, two typical cases are studied, one with the exact traveling wave solutions, yielding the values of speeds, the other with the series expansion solution, also yielding the value of speed. Conversely, when the exponent of creation term is smaller than the one of the annihilation term, two typical cases are also studied, but only for one of them, there is a series development solution, yielding the value of speed, and for the other, traveling wave solution cannot exist. Besides, the formula of caculating speeds and solutions of planar wave within the thin boundary layer are given for a class of typical excitable media.

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Authors and Affiliations

  1. Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, 100080, Beijing, P R China

    Zhou Tian-shou & Zhang Suo-chun

Authors
  1. Zhou Tian-shou
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  2. Zhang Suo-chun
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Additional information

Communicated by Dai Shi-qiang

Foundation item: the National Natural Science Foundation of China (19901034)

Biography: Zhou Tian-shou (1962-), Associate Professor, Doctor

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Tian-shou, Z., Suo-chun, Z. Traveling wave speed and solution in reaction-diffusion equation in one dimension. Appl Math Mech 22, 674–681 (2001). https://doi.org/10.1007/BF02435667

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  • DOI: https://doi.org/10.1007/BF02435667

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