| Abstract: |
| We consider the road-field reaction-diffusion model introduced by Berestycki, Roquejoffre, and Rossi. By performing a thin-front limit, we deduce a Hamilton-Jacobi equation with a suitable effective Hamiltonian on the road that governs the front location in the road-field model. Our main motivation is to apply the theory of strong (flux-limited) viscosity solutions to obtain a control-theoretic interpretation of the front location. We then formulate the ecological invasion problem as one of finding optimal paths that balance the positive growth rate in the field with the fast diffusion on the road. Along the way, we extend the results of Berestycki et al. to conical domains and exhibit non-convex expansion shapes. We also provide a new proof of known results for the one-road half-space problem using our approach. This is joint work with Chris Henderson. |
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