任意阶自催化反应扩散系统的正平衡态

Positive Steady States in a Reaction-Diffusion System with Arbitrary Powers of Autocatalysis

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.

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.