Sticky-reflecting diffusion as a Wasserstein gradient flow
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912201593323520 |
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| author | Casteras, Jean-Baptiste Monsaingeon, Léonard Santambrogio, Filippo |
| author_facet | Casteras, Jean-Baptiste Monsaingeon, Léonard Santambrogio, Filippo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_16842 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sticky-reflecting diffusion as a Wasserstein gradient flow Casteras, Jean-Baptiste Monsaingeon, Léonard Santambrogio, Filippo Analysis of PDEs Optimization and Control 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. |
| title | Sticky-reflecting diffusion as a Wasserstein gradient flow |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2401.16842 |