Time-periodic branched transport
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915693229768704 |
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| author | Kitagawa, Jun Mikat, Cecilia |
| author_facet | Kitagawa, Jun Mikat, Cecilia |
| contents | We develop a new framework for branched transport between probability measures which are allowed to vary in time. This framework can be used to model problems where the underlying transportation network displays a branched structure, but the source and target mass distributions can change cyclically over time, such as road networks or circulatory systems. We introduce the notion of time-dependent transport paths along with associated energies and distances, and prove existence of transport paths whose energy achieves the distance. We also show the time-dependent transport yields a metric structure on subsets of appropriately defined measure-valued Sobolev spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_10498 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Time-periodic branched transport Kitagawa, Jun Mikat, Cecilia Optimization and Control Metric Geometry 28B05, 49Q20, 49Q10, 90B10 We develop a new framework for branched transport between probability measures which are allowed to vary in time. This framework can be used to model problems where the underlying transportation network displays a branched structure, but the source and target mass distributions can change cyclically over time, such as road networks or circulatory systems. We introduce the notion of time-dependent transport paths along with associated energies and distances, and prove existence of transport paths whose energy achieves the distance. We also show the time-dependent transport yields a metric structure on subsets of appropriately defined measure-valued Sobolev spaces. |
| title | Time-periodic branched transport |
| topic | Optimization and Control Metric Geometry 28B05, 49Q20, 49Q10, 90B10 |
| url | https://arxiv.org/abs/2511.10498 |