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arXiv · 2401.16842

Sticky-reflecting diffusion as a Wasserstein gradient flow

Jean-Baptiste Casteras·Léonard Monsaingeon·Filippo Santambrogio
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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.

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Jean-Baptiste Casteras, Léonard Monsaingeon, Filippo Santambrogio. 2025-01-24. Sticky-reflecting diffusion as a Wasserstein gradient flow. https://arxiv.org/abs/2401.16842

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