A free boundary problem of a predator–prey model with a nonlocal reaction term

Abstract

This paper is devoted to classifying the dynamical behavior of solutions to a free boundary problem of a predator–prey model with a nonlocal reaction term. We investigate the spreading-vanishing dichotomy, that is, the asymptotic behavior of predator and prey species. Moreover, some criteria are also established for spreading and vanishing. At last, when spreading occurs, we obtain an upper and a lower bound of the asymptotic spreading speed.