Dynamics for the diffusive mutualist model with advection and different free boundaries

Abstract

In this paper, we study the diffusive mutualist model with advection and different free boundaries in one space dimension. These two free boundaries may intersect each other as time evolves and can be used to describe the spreading of invasive and native species directly. We first prove the existence and uniqueness, regularity and uniform estimates of global solution. Then we provide the criteria governing spreading and vanishing. At last we investigate long time behaviors and asymptotic spreading speeds of two species and asymptotic speeds of two free boundaries.