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math.AP2025
The field-road diffusion model: fundamental solution and asymptotic behavior
Matthieu Alfaro, Romain Ducasse, Samuel Tréton
We consider the linear field-road system, a model for fast diffusion channels in population dynamics and ecology. This system takes the form of a system of PDEs set on domains of d…
math.AP2024
Propagation or extinction in bistable equations: the non-monotone role of initial fragmentation
Matthieu Alfaro, François Hamel, Lionel Roques
In this paper, we investigate the large-time behavior of bounded solutions of the Cauchy problem for a reaction-diffusion equation in with bistable reaction term. We…