Note on a two-species competition-diffusion model with two free boundaries

In Guo and Wu (2015) and Wu (2015), the authors studied a two-species competition-diffusion model with two free boundaries. These two free boundaries describing the spreading fronts of two competing species, respectively, may intersect each other as time evolves. The existence, uniqueness and long time behavior of global solution have been established. In this note we discuss the conditions for spreading and vanishing, and more accurate limits of (u,v) as t→∞ when spreading occurs. Some new results and simpler proofs will be provided.