| 一类反应扩散方程的分歧分析 |
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| 引用本文： | 王华涛.一类反应扩散方程的分歧分析[J].内江师范学院学报,2009,24(12):20-23. |
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| 作者姓名： | 王华涛 |
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| 作者单位： | 四川大学数学学院,四川,成都610065 |
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| 摘 要： | 讨论了一类反应扩散方程的分歧（分岔）现象．运用一般线性全连续场谱定理和L—S（李雅普诺夫-施密特）约化方法得到了此方程的一阶近似形式并求出了从平凡解分歧出的非平凡解的具体表达式．最后运用一些经典分歧定理得到了一些重要的分歧结果，给出了分歧图形．
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| 关 键 词： | 反应扩散 L-S约化方法 谱定理 一阶近似 分歧 |
Bifurcation Analysis of One Class of Reaction-diffusion Equations |
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| WANG Hua-tao.Bifurcation Analysis of One Class of Reaction-diffusion Equations[J].Journal of Neijiang Teachers College,2009,24(12):20-23. |
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| Authors: | WANG Hua-tao |
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| Institution: | WANG Hua-tao (College of Mathemaetics, Sichuan University, Chengdu 610065, China) |
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| Abstract: | The bifurcation phenomena of reaction-diffusion equations are investigated. By using the Spectrum Theorem of the general completely continuous linear operator and the Reduction method of L-S（Lyapunov-Schmdt）, the first-order approximation equation of such reaction-diffusion equations is obtained. In addition, the specific expression of the nontrivial solu- tion is determined via the bifurcation of its trivial solution. And by applying some of the classic bifurcation theorems some important bifurcation results are found with their respective bifurcation diagrams given in the end. |
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| Keywords: | reaction-diffusion L-S reduction method spectrum theorem first-order approximation bifurcation |
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