Qualitative Analysis Of A Predator-prey Model With A Free Boundary

In this paper we consider an initial boundary problem of the prey-predator model with a free boundary in one space dimension.The main purpose is to study the long time behavior of the predator and the prey in this model.Firstly,we get the spreading-vanishing dichotomy,which implies that the two species either obtain the successful development as the time t goes to infinity,such that they successfully survive in the new environment, or they fail to spread and die in the long time .Secondly, the criteria for the development of the two species are given.Finally, when the species can be successfully developed, we give an estimate for the spreading speed.