In this paper we investigate a class of two-species invasion models with a free boundary and with cross-diffusion and self-diffusion in interval $[0,+\infty )$, where the native species occupies the whole environment $[0,+\infty )$, and the invasion species invade into the habitat of the native species. The systems under consideration are strongly coupled, and the position of the free boundary is determined by the Stefan condition. The aim of this paper is to show the existence of a global classical solution for the free boundary problems by using suitable transformations, the contraction mapping theorem and various estimates. Applications are given to the classical competition and predator-prey models with cross-diffusion and self-diffusion.

在本文中，我们研究了一类具有自由边界并且在区间内具有交叉扩散和自扩散的两种种群入侵模型。 $[0，+\infty ）$，本地物种占据整个环境 $[0，+\infty ）$，入侵物种侵入本地物种的栖息地。所考虑的系统是强耦合的，自由边界的位置由Stefan条件确定。本文的目的是通过使用适当的变换，压缩映射定理和各种估计来证明自由边界问题的全局经典解的存在。具有交叉扩散和自扩散的经典竞争和捕食者－食饵模型得到了应用。