A Reaction-Diffusion-Advection Equation with a Free Boundary and Sign-Changing Coefficient

In this paper we investigate a reaction-diffusion-advection equation with a free boundary and sign-changing coefficient. The main objective is to understand the influence of the advection term on the long time behavior of the solutions. More precisely, we prove a spreading-vanishing dichotomy result, namely the species either successfully spreads to infinity as t → ∞ and survives in the new environment, or it fails to establish and dies out in the long run. When spreading occurs, the spreading speed of the expanding front is affected by the advection. In this situation, we obtain best possible upper and lower bounds for the spreading speed of the expanding front. Furthermore, when the environment is asymptotically homogeneous at infinity, these two bounds coincide.