  This short paper concerns a diffusive logistic equation with the
heterogeneous environment and a free boundary, which is formulated to study the
spread of an invasive species, where the free boundary represents the expanding
front. A spreading-vanishing dichotomy is derived, namely the species either
successfully spreads to the right-half-space as time $t\to\infty$ and survives
(persists) in the new environment, or it fails to establish and will extinct in
the long run. The sharp criteria for spreading and vanishing is also obtained.
When spreading happens, we estimate the asymptotic spreading speed of the free
boundary.
