Traveling Wave Speed and Solution in Reaction-Diffusion Equation in One Dimension

ZHOU Tian-shou; ZHANG Suo-chun

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ZHOU Tian-shou, ZHANG Suo-chun. Traveling Wave Speed and Solution in Reaction-Diffusion Equation in One Dimension[J]. Applied Mathematics and Mechanics, 2001, 22(6): 602-608.

Citation:

ZHOU Tian-shou, ZHANG Suo-chun. Traveling Wave Speed and Solution in Reaction-Diffusion Equation in One Dimension[J]. Applied Mathematics and Mechanics, 2001, 22(6): 602-608.

Citation:

ZHOU Tian-shou, ZHANG Suo-chun. Traveling Wave Speed and Solution in Reaction-Diffusion Equation in One Dimension[J]. Applied Mathematics and Mechanics, 2001, 22(6): 602-608.

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Traveling Wave Speed and Solution in Reaction-Diffusion Equation in One Dimension

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

Received Date: 1999-09-20
Rev Recd Date: 2001-02-27
Publish Date: 2001-06-15

Abstract

Abstract

By Painlev 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 calculating speeds and solutions of planar wave within the thin boundary layer are given for a class of typical excitable media.
- Painlev analysis,
- traveling wave,
- excitable media

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References(11)

References

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