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.
