  We consider the road-field reaction-diffusion model introduced by Berestycki,
Roquejoffre, and Rossi. By performing a "thin-front limit," we are able to
deduce a Hamilton-Jacobi equation with a suitable effective Hamiltonian on the
road that governs the front location of the road-field model. Our main
motivation is to apply the theory of strong (flux-limited) viscosity solutions
in order to determine a control formulation interpretation of the front
location. In view of the ecological meaning of the road-field model, this is
natural as it casts the invasion problem as one of finding optimal paths that
balance the positive growth rate in the field with the fast diffusion on the
road.
  Our main contribution is a nearly complete picture of the behavior on
two-road conical domains. When the diffusivities on each road are the same, we
show that the propagation speed in each direction in the cone can be computed
via those associated with one-road half-space problem. When the diffusivities
differ, we show that the speed along the faster road is unchanged, while the
speed along the slower road can be enhanced. Along the way we provide a new
proof of known results on the one-road half-space problem via our approach.
