Issue |
ESAIM: COCV
Volume 29, 2023
|
|
---|---|---|
Article Number | 54 | |
Number of page(s) | 23 | |
DOI | https://doi.org/10.1051/cocv/2023027 | |
Published online | 18 July 2023 |
Dynamic Optimal Transport on Networks
1
Computational Imaging Group and Helmholtz Imaging, Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany
2
Westfälische Wilhelms-Universität (WWU) Münster, Institute for Analysis and Computational Mathematics, Germany
3
University of Augsburg, Institute of Mathematics, MNTF, Augsburg, Germany
* Corresponding author: jan.pietschmann@gmail.com
Received:
16
September
2022
Accepted:
7
April
2023
We study a dynamic optimal transport problem on a network. Despite the cost for transport along the edges, an additional cost, scaled with a parameter κ, has to be paid for interchanging mass between edges and vertices. We show existence of minimisers using duality and discuss the relationship of the model to other metrics such as Fisher–Rao and the classical Wasserstein metric. Finally, we examine the limiting behaviour of the model in terms of the parameter κ.
Mathematics Subject Classification: 35R02 / 49Q22 / 60B05
Key words: Metric graph / optimal transport / gradient flow / convex duality / entropy
© The authors. Published by EDP Sciences, SMAI 2023
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