A Free Boundary Problem for a Ratio-dependent Predator-prey System

In this paper we study a free boundary problem for a ratio-dependent predator-prey system in one space dimension, with the free boundary only caused by the prey. The long time behaviors of solution are discussed. Then we establish a spreading-vanishing dichotomy and the criteria for spreading and vanishing. Finally, when spreading occurs, an accurate limit of the asymptotic speed of h(t) is provided.