一类自催化反应扩散模型正解的唯一性与稳定性(英文)

Uniqueness and Stability for Positive Solutions of a Reaction-Diffusion Model with Autocatalysis

主要考虑了一类三分子自催化反应扩散系统.在齐次Dirichlet和Robin边界条件下,当反应率c适当小,系统没有共存态;当c适当大,系统至少有一个共存态;当c充分大,系统有唯一渐近稳定的共存态.特别地,在一维空间上共存态是唯一的.在齐次Neumann边界条件下系统是一个简单系统.

In the paper, a tri-molecular autocatalytic reaction-diffusion system with different boundary conditions is investigated. Under the boundary conditions of Dirichlet type or Robin type, it turns out that if the parameter c （the reaction rate） is properly small, then the system has no coexistence state, if the parameter c is suitably large, then the system has at least one coexistence state, and if the parameter c is sufficiently large, then the coexistence state is unique and asymptotically stable. In particular, it is also proven that the system has unique coexistence state in the onedimension domain. Under the boundary condition of Neumann type, it turns out that the dynamics system is simple.