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math.AP2026
A functional inequalities approach for the field-road diffusion model with (symmetric) nonlinear exchanges
Matthieu Alfaro, Claire Chainais-Hillairet, Flore Nabet
In this note, we consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions and coupled through (…
math.AP2024
Bridging bulk and surface: An interacting particle system towards the field-road diffusion model
Matthieu Alfaro, Mustapha Mourragui, Samuel Tréton
We recover the so-called field-road diffusion model as the hydrodynamic limit of an interacting particle system. The former consists of two parabolic PDEs posed on two sets of diff…
math.AP2023
Long time behavior of the field-road diffusion model: an entropy method and a finite volume scheme
Matthieu Alfaro, Claire Chainais-Hillairet
We consider the so-called field-road diffusion model in a bounded domain, consisting of two parabolic PDEs posed on sets of different dimensions (a {\it field} and a {\it road} in…