Title: Optimal Transport and Gradient Flows on Network
Abstract: In this talk we will discuss the mathematical modelling and analysis of optimal transport problems
on networks, which we perceive as metric graphs possibly augmented with variables on the nodes.
Such problems have various applications such as e.g. urban traffic with crossings representing nodes or
transport in gas network. The transport problems and related distances such as Wasserstein metrics on
the network are a basis to define metric gradient flows and we will discuss some basic properties and
examples. Finally we will give an outlook to related Port-Hamiltonian structures extending the metric
gradient flows.
(Host: Markus Bachmayr)