A REACTION-DIFFUSION-ADVECTION TWO-SPECIES COMPETITION SYSTEM WITH A FREE BOUNDARY IN HETEROGENEOUS ENVIRONMENT

In this paper, we investigate a reaction-diffusion-advection two species competition system with a free boundary in heterogeneous environment. The primary aim is to study the impact of small advection terms and heterogeneous environment, which is on two species' dynamics via a free boundary. The function m(x) represents heterogeneous environment, and it can satisfy positive everywhere condition or changeable sign condition. Firstly, on one hand, we provide long time behaviors of the solution in vanishing case when m(x) satisfies both conditions above; on the other hand, long time behaviors of the solution in spreading case are got when m(x) satisfies positive everywhere condition. Secondly, a spreading-vanishing dichotomy and several sufficient conditions through the initial data and the moving parameters are obtained to determine whether spreading or vanishing of two species happens when m(x) satisfies both conditions above. Furthermore, we derive estimates of spreading speed of the free boundary when m(x) satisfies positive everywhere condition and two species spreading occurs.