一类自催化反应扩散模型共存解的分析

摘要

An autocatalytic reaction-diffusion system is investigated. The coexistence states of the system is considered by using the degree theory, under the boundary conditions of Dirichlet type.Regarding the reaction rate c as the bifurcation parameter, the subcritical and supcritical bifurcations are determined. It is shown that if c is properly small, then the system has nocoexistence state, and if c is sufficiently large, then the system has at least one coexistence state. The existence of subcritical bifurcation turns out that the system has at least two coexistence states by global bifurcation theory.%研究了带有饱和项的自催化反应扩散模型的共存解.在齐次Dirichlet边界条件下,运用度理论方法证明了系统正解的存在性.把转化率c看作分歧参数,给出了系统存在超临界和次临界分歧的条件.结果表明:转化率适当小时系统没有共存态,转化率充分大时系统一定有共存态.此外,当系统存在次临界分歧时,利用全局分歧理论可知系统至少存在两个共存态.