| 一维反应扩散方程中的行波波速及行波解 |
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| 引用本文： | 周天寿,张锁春. 一维反应扩散方程中的行波波速及行波解[J]. 应用数学和力学, 2001, 22(6): 602-608 |
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| 作者姓名： | 周天寿 张锁春 |
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| 作者单位： | 中国科学院数学与系统科学研究院, 应用数学研究所, 北京100080 |
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| 基金项目： | 国家自然科学基金资助项目(19901034) |
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| 摘 要： | 通过Painlev啨分析,详细研究了一类一维化学反应扩散方程中的行波解及波速。分别给出了当歼灭项的指数大于创造项的指数及创造项的指数大于歼灭项的指数时,这两种情形下的波速及行波解的显式表示。此外,还给出了一类常见激励介质中的波速及平面波解在薄的边界层内的公式。
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| 关 键 词： | Painlev啨分析 行波 激励介质 |
| 文章编号： | 1000-0887(2001)06-0602-07 |
| 收稿时间： | 1999-09-20 |
| 修稿时间： | 1999-09-20 |
Traveling Wave Speed andSolution in Reaction- Diffusion Equation in One Dimension |
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| ZHOU Tian-Shou,ZHANG SUO-CHUN. Traveling Wave Speed andSolution in Reaction- Diffusion Equation in One Dimension[J]. Applied Mathematics and Mechanics, 2001, 22(6): 602-608 |
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| Authors: | ZHOU Tian-Shou ZHANG SUO-CHUN |
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| Affiliation: | Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, P R China |
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| Abstract: | By Painlevé analysis, traveling wave s p eed and solution of reaction-diffusion equations for the concentration of one sp ecies 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 c ases are studied, one with the exact traveling wave solutions, yielding the valu es of speeds, the other with the series expansion solution, also yielding the va l ue 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 o ne 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 o f calculating speeds and solutions of planar wave within the thin boundary layer are given for a class of typical excitable media. |
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