An optimization problem for mass transportation with congested dynamics
Résumé
Starting from the work by Brenier and Benamou, where a dynamic formulation of mass transportation problems was given, we consider a more general framework, where different kind of cost functions are allowed. This seems relevant in some problems presenting congestion effects as for instance traffic on a highway, crowds moving in domains with obstacles, and in general in all cases where the transportation does not behave as in the classical Monge setting. We show some numerical computations obtained by generalizing to our framework the scheme introduced in Benamou and Brenier.
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