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

Spreading speeds and pulsating fronts for a field-road model in a spatially periodic habitat