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Variational models for transportation networks: old and new formulations

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DNMW04 - New trends and challenges in the mathematics of optimal design

A small number of models for transportation networks (modelling street, river, or vessel networks, for instance) has been studied intensely during the past decade, in particular the so-called branched transport and the so-called urban planning. They assign to each network the total cost for transporting material from a given initial to a prescribed final distribution and seek the cost-optimal network. Typically, the considered transportation cost per mass is smaller the more mass is transported together, which leads to highly patterned and ramified optimal networks. I will present novel formulations of these models which allow a better interpretation as an optimal design problem.

This talk is part of the Isaac Newton Institute Seminar Series series.

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