一类多孔介质型扩散互惠模型的共存态和渐近性

研究了一类具有多孔介质型扩散的3种群互惠模型Dirichlet边值问题.在适当的条件下,证明了该时变问题存在唯一有界整体解,且除了平凡解和半平凡解之外,相应的平衡态问题还存在正的最大解和最小解.此外,该时变解在一些初值函数下收敛到最大平衡解,而在另一些初值函数下收敛到最小平衡解.这种收敛性对反应函数的任意系数都成立.该结果意味着带多孔介质型扩散的互惠模型的动力学性态不同于带常数扩散项的.

Coexistence and Asymptotic Behavior of a Cooperating Model with Porous Medium Type of Diffusion

This paper deals with a Dirichlet boundary value problem for a three-species cooperating model with porous medium type of diffusion.It is proved that the time-dependent problem possesses a unique bounded global solution under appropriate conditions;and in addition to the trivial and semi-trivial solutions,there exists a positive maximal solution and a positive minimal solution to the corresponding steady state problem.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.The results indicate that the dynamic behavior of a cooperating model with porous medium type of diffusion can be quite different from the model with constant diffusion terms.