Article Dans Une Revue Journal of Mathematical Sciences Année : 2014

A continuous model of transportation revisited

Résumé

We review two models of optimal transport, where congestion eff ects during the transport can be possibly taken into account. The first model is Beckmann's one, where the transport activities are modeled by vector fi elds with given divergence. The second one is the model by Carlier et al. (SIAM J Control Optim 47: 1330--1350, 2008), which in turn is the continuous reformulation of Wardrop's model on graphs. We discuss the extensions of these models to their natural functional analytic setting and show that they are indeed equivalent, by using Smirnov decomposition theorem for normal $1-$currents.

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Dates et versions

hal-00758565 , version 1 (28-11-2012)
hal-00758565 , version 2 (01-02-2013)

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  • HAL Id : hal-00758565 , version 2

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Lorenzo Brasco, Mircea Petrache. A continuous model of transportation revisited. Journal of Mathematical Sciences, 2014, 196, pp.119-137. ⟨hal-00758565v2⟩
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