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Evolution Models for Mass Transportation Problems

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Abstract

We present a survey on several mass transportation problems, in which a given mass dynamically moves from an initial configuration to a final one. The approach we consider is the one introduced by Benamou and Brenier in [5], where a suitable cost functional F(ρ, v), depending on the density ρ and on the velocity v (which fulfill the continuity equation), has to be minimized. Acting on the functional F various forms of mass transportation problems can be modeled, as for instance those presenting congestion effects, occurring in traffic simulations and in crowd motions, or concentration effects, which give rise to branched structures.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo, 5, 56127, Pisa, Italy

    Giuseppe Buttazzo

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  1. Giuseppe Buttazzo
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Correspondence to Giuseppe Buttazzo.

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This work is part of the project 2008K7Z249 Trasporto ottimo di massa, disuguaglianze geometriche e funzionali e applicazioni financed by the Italian Ministry of Research.

Lecture held in the Seminario matematico e Fisico on February 14, 2011

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Buttazzo, G. Evolution Models for Mass Transportation Problems. Milan J. Math. 80, 47–63 (2012). https://doi.org/10.1007/s00032-012-0175-x

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