Transport equation with source and generalized Wasserstein distance

Benedetto Piccoli 1
1 Rutgers University, Department of Mathematics
Department of Mathematics - Rutgers School of Arts and Sciences
Abstract : 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.
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Benedetto Piccoli. Transport equation with source and generalized Wasserstein distance. NETCO 2014 - New Trends in Optimal Control, Jun 2014, Tours, France. ⟨hal-01031203⟩

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