一类生化反应扩散系统的模式生成

Pattern formation of a class of biochemical reaction-diffusion system

考虑一类具扩散的生化反应系统的平衡态问题,获得该模型正平衡态解的一些结果.给出正解的先验估计,用能量方法得到其非常数正解的不存在性,用拓扑度理论得出其非常数正解(即模式)的存在性结论.

The steady-state problem of a class of diffusive biochemical reaction system was taken into consideration and some results of positive steady-state solutions of this problem were obtained. Firstly, a priori estimates was given for the positive solutions and then the non-existence of non-constant positive solutions was obtained by using the energy method, and further the existence of non-constant positive solutions （namely, patterns） was obtained by using the topological degree theory.