In this paper, we investigate a reaction–diffusion–advection equation with a free boundary which models the spreading of an invasive species in one-dimensional heterogeneous environments. We assume that the species has a tendency to move upward along the resource gradient in addition to random dispersal, and the spreading mechanism of species is determined by a Stefan-type condition. Investigating the sign of the principal eigenvalue of the associated linearized eigenvalue problem, under certain conditions we obtain the sharp criteria for spreading and vanishing via system parameters. Also, we establish the long-time behavior of the solution and the asymptotic spreading speed. Finally, some biological implications are discussed.
- Free boundary problem
- Heterogeneous environments
- Population dynamics
- Reaction–diffusion–advection equation