In this paper we consider a class of diffusive ecological models with two free boundaries and with cross-diffusion and self-diffusion in one space dimension. The systems under consideration are strongly coupled, and the position of each free boundary is determined by the Stefan condition. We first show local existence of the solutions for the ecological models under some assumptions, and then prove the global existence of the solutions under extra assumptions. Our approach to the problem is by suitable changes, fixed point theorems and various estimates. Applications of these results are given to a two-species diffusive predator–prey model and a two-species diffusive competition model.

在本文中，我们考虑一类具有两个自由边界并且在一个空间维度上具有交叉扩散和自扩散的扩散生态模型。所考虑的系统是强耦合的，每个自由边界的位置由Stefan条件确定。我们首先显示在某些假设下该生态模型解的局部存在，然后在额外假设下证明该解的全局存在。我们通过适当的更改，不动点定理和各种估计来解决问题。将这些结果应用于两种种群的扩散捕食－被捕食模型和两种种群的扩散竞争模型。