Evolution models for mass transportation problems

Details Evolution models for mass transportation problems Evolution models for mass transportation problems

2012-04-07

arxiv.org/abs/1204.1660v1

Mathematics

Optimization and Control

16 pages, 14 figures; Milan J. Math., (2012)

Scientific paper

10.1007/s00032-012-0175-x

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 $F(\rho,v)$, depending on the density $\rho$ 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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