2021/01/09 by Burger, Martin, Humpert, Ina, Pietschmann, Jan-Frederik · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2101.03415
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 f 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.