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Pré-Publication, Document De Travail Année : 2024

Sticky-reflecting diffusion as a Wasserstein gradient flow

Résumé

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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Dates et versions

hal-04427686 , version 1 (31-01-2024)

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  • HAL Id : hal-04427686 , version 1

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Jean-Baptiste Casteras, Filippo Santambrogio, Leonard Monsaingeon. Sticky-reflecting diffusion as a Wasserstein gradient flow. 2024. ⟨hal-04427686⟩
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