A functional inequalities approach for the field-road diffusion model with (symmetric) nonlinear exchanges
Analysis of PDEs
2026-01-21 v1
Abstract
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 (symmetric) nonlinear exchange terms. We propose a new and rather direct functional inequalities approach to prove the exponential decay of a relative entropy, and thus the convergence of the solution towards the stationary state selected by the total mass of the initial datum.
Cite
@article{arxiv.2601.12909,
title = {A functional inequalities approach for the field-road diffusion model with (symmetric) nonlinear exchanges},
author = {Matthieu Alfaro and Claire Chainais-Hillairet and Flore Nabet},
journal= {arXiv preprint arXiv:2601.12909},
year = {2026}
}