Sticky-reflecting diffusion as a Wasserstein gradient flow
Analysis of PDEs
2025-01-27 v2 Optimization and Control
Abstract
In this paper we identify the Fokker-Planck equation for (reflected) Sticky Brownian Motion as a Wasserstein gradient flow in the space of probability measures. The driving functional is the relative entropy with respect to a non-standard reference measure, the sum of an absolutely continuous interior part plus a singular part supported on the boundary. Taking the small time-step limit in a minimizing movement (JKO scheme) we prove existence of weak solutions for the coupled system of PDEs satisfying in addition an Energy Dissipation Inequality.
Cite
@article{arxiv.2401.16842,
title = {Sticky-reflecting diffusion as a Wasserstein gradient flow},
author = {Jean-Baptiste Casteras and Léonard Monsaingeon and Filippo Santambrogio},
journal= {arXiv preprint arXiv:2401.16842},
year = {2025}
}
Comments
accepted for publication in JMPA