| 任意阶自催化反应扩散系统的正平衡态 |
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| 引用本文： | 鲁元海.任意阶自催化反应扩散系统的正平衡态[J].汕头大学学报(自然科学版),2013(1):14-21. |
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| 作者姓名： | 鲁元海 |
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| 作者单位： | 中山市东区中学 |
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| 摘 要： | 研究了一个任意阶自催化反应扩散系统的正平衡态.在解的先验估计基础上,利用隐函数定理及拓扑度理论,获得了该系统非常数正平衡态解的不存在性与存在性结论.结果表明,在一个化学反应系统中,不同的扩散系数或催化剂阶数对系统的模式生成起着不同的作用.
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| 关 键 词： | 自催化化学系统 任意阶催化剂 Leray-Schauder度 正平衡态 |
Positive Steady States in a Reaction-Diffusion System with Arbitrary Powers of Autocatalysis |
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| LU Yuan-hai.Positive Steady States in a Reaction-Diffusion System with Arbitrary Powers of Autocatalysis[J].Journal of Shantou University(Natural Science Edition),2013(1):14-21. |
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| Authors: | LU Yuan-hai |
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| Institution: | LU Yuan-hai(Dongqu Middle School of Zhongshan,Zhongshan 528403,Guangdong,China) |
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| Abstract: | Positive steady states in a reaction-diffusion system with arbitrary powers of autocatalysis are considered.Based on a priori estimates,non-existence and existence of non-constant positive steady state solutions are shown by using implicit function theorem and topological degree theory,respectively.The results show that in a chemical model,different diffusions or autocatalysis orders may play essentially different roles in developing spatial patterns. |
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| Keywords: | autocatalytic chemical system arbitrary powers of autocatalysis Leray-Schauder degree positive steady states |
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