A free boundary problem with impulsive harvesting in small advection environment

This paper is devoted to the study of the combined effects of impulsive harvesting and small advection on the dynamical behavior of solutions to a free boundary model. By introducing a one-parameter family of initial data $\sigma \varphi$ with $\sigma \ge 0$ and $\varphi$ being a compactly supported function, under some suitable assumptions, we obtain a threshold value ${\sigma }^{\ast }$ such that spreading happens when $\sigma >{\sigma }^{\ast }$, vanishing happens when $\sigma \le {\sigma }^{\ast }$.