  A reaction-diffusion model which is called the field-road model was
introduced by Berestycki, Roquejoffre and Rossi [9] to describe biological
invasion with fast diffusion on a line. In this paper, we investigate this
model in a heterogeneous landscape and establish the existence of the
asymptotic spreading speed c * as well as its coincidence with the minimal wave
speed of pulsating fronts along the road. We start with a truncated problem
with an imposed Dirichlet boundary condition. We prove the existence of
spreading speed c * R which coincides with the minimal speed of pulsating
fronts for the truncated problem in the direction of the road. The arguments
combine the dynamical system method with PDE's approach. Finally, we turn back
to the original problem in the half-plane via generalized principal eigenvalue
approach as well as an asymptotic method.
