Optimal regions for congested transport∗
1 Dipartimento di Matematica, Università di Pisa, Largo B.
Pontecorvo 5, 56126 Pisa, Italy.
2 CEREMADE UMR CNRS 7534, Université de Paris Dauphine, Pl. de Lattre de Tassigny, 75775 Paris cedex 16, France.
We consider a given region Ω where the traffic flows according to two regimes: in a region C we have a low congestion, where in the remaining part Ω \ C the congestion is higher. The two congestion functions H1 and H2 are given, but the region C has to be determined in an optimal way in order to minimize the total transportation cost. Various penalization terms on C are considered and some numerical computations are shown.
Mathematics Subject Classification: 49Q20 / 49Q10 / 90B20
Key words: Shape optimization / transport problems / congestion effects / optimal networks
The work of the first and third authors is part of the project 2010A2TFX2 “Calcolo delle Variazioni” funded by the Italian Ministry of Research and University. The second author gratefully acknowledges the support of INRIA and the ANR through the Projects ISOTACE (ANR-12-MONU-0013) and OPTIFORM (ANR-12-BS01-0007).
© EDP Sciences, SMAI 2015