Optimal transport on gas networks
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917993386082304 |
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| author | Fazeny, Ariane Burger, Martin Pietschmann, Jan-Frederik |
| author_facet | Fazeny, Ariane Burger, Martin Pietschmann, Jan-Frederik |
| contents | This paper models gas networks as metric graphs, with isothermal Euler equations at the edges, Kirchhoff's law at interior vertices and time-(in)dependent boundary conditions at boundary vertices. For this setup, a generalized $p$-Wasserstein metric in a dynamic formulation is introduced and utilized to derive $p$-Wasserstein gradient flows, specifically focusing on the non-standard case $p = 3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01698 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal transport on gas networks Fazeny, Ariane Burger, Martin Pietschmann, Jan-Frederik Analysis of PDEs Optimization and Control 49Q22, 35R02, 76N25 (Primary) 35Q35, 60B05 (Secondary) This paper models gas networks as metric graphs, with isothermal Euler equations at the edges, Kirchhoff's law at interior vertices and time-(in)dependent boundary conditions at boundary vertices. For this setup, a generalized $p$-Wasserstein metric in a dynamic formulation is introduced and utilized to derive $p$-Wasserstein gradient flows, specifically focusing on the non-standard case $p = 3$. |
| title | Optimal transport on gas networks |
| topic | Analysis of PDEs Optimization and Control 49Q22, 35R02, 76N25 (Primary) 35Q35, 60B05 (Secondary) |
| url | https://arxiv.org/abs/2405.01698 |