Spreading dynamics for the diffusive competition model with free boundary and time delay

In this paper, we focus on the global dynamics and asymptotic spreading speed for a diffusive Lotka-Volterra type competition system with free boundary and time delay. The well-posedness of solution is established, and some sufficient conditions for spreading and vanishing are derived by giving a suitable initial value compatibility condition. When spreading persists, the asymptotic spreading speed for the invasive species is given by studying an associated semi-wave problem. It is shown that time delay can slow down the spreading speed.