Long time behavior of solutions of a diffusion–advection logistic model with free boundaries

In this paper, we study the long behavior of solutions of a diffusion–advection logistic model with free boundaries in one dimensional space when the influence of advection is small. We give a spreading–vanishing dichotomy for this model, that is, the solution either converges to 1 locally uniformly in RR, or to 0 uniformly in its occupying domain. Moreover, by introducing a parameter σσ in the initial data, we exhibit the sharp threshold between vanishing and spreading, that is, there exists a value σ∗σ∗ such that spreading happens when σ>σ∗σ>σ∗, vanishing happens when σ≤σ∗σ≤σ∗.