Optimal regions for congested transport
Buttazzo, Giuseppe1 ; Carlier, Guillaume2 ; Lo Bianco, Serena Guarino1
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.
ESAIM: Mathematical Modelling and Numerical Analysis , Optimal Transport, Tome 49 (2015) no. 6, pp. 1607-1619.

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 H 1 and H 2 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.

Reçu le :
DOI : 10.1051/m2an/2015022
Classification : 49Q20, 49Q10, 90B20
Mots-clés : Shape optimization, transport problems, congestion effects, optimal networks
Buttazzo, Giuseppe 1 ; Carlier, Guillaume 2 ; Lo Bianco, Serena Guarino 1

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. 
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Buttazzo, Giuseppe; Carlier, Guillaume; Lo Bianco, Serena Guarino. Optimal regions for congested transport. ESAIM: Mathematical Modelling and Numerical Analysis , Optimal Transport, Tome 49 (2015) no. 6, pp. 1607-1619. doi : 10.1051/m2an/2015022. http://www.numdam.org/articles/10.1051/m2an/2015022/

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