关键词: 互惠模型, 退缩, 扩散, 共存态, 渐近性, 多孔介质

Abstract: For a two-species mutualistic model, if the degenerate diffusion terms are[-upΔu] and [-vqΔv]then for a certain set of reaction rates in the reaction function the solution of the model blows up in finite time, and for another set of reaction rates, a unique global solution exists. In this paper, it proves that if the diffusion terms are[-Δum]and[-Δvn]then the dynamic behavior of the solution can be quite different. For this model, under appropriate conditions, the time-dependent problem has a unique bounded global solution, and the corresponding steady-state problem has a positive maximal solution and a positive minimal solution. Moreover, the time-dependent solution converges to the maximal solution for one class of initial functions, and to the minimal solution for another class of initial functions. The above convergence property holds true for any reaction rates in the reaction function. This means the dynamic behavior of a mutualistic model with different degenerate diffusion terms can be different.