Transport equation with source and generalized Wasserstein distance
Résumé
We will start by revising some macroscopic model, based on systems of conservation (or balance) laws, for network flows, such as road networks, supply chains, gas pipelines etc.. Such models were successfully employed in traffic monitoring projects. Then we will pass to measure solutions to nonlinear transport equations, which naturally allow multi-scale approaches. In particular we can integrate micro and macro scales in a unique representation. We show how the Wasserstein metric is the natural one in this context and how to generalize it to deal with source terms. Finally, we show some examples of simulations for crowd dynamics and vehicular traffic.
Domaines
Optimisation et contrôle [math.OC]
Origine : Fichiers produits par l'(les) auteur(s)