Transport of measures on networks

Venue: Seminar Room "-1" – Via Sommarive, 14 Povo - Trento
Hour: 12.15 a.m.

• Gabriele Caselli - PhD in Mathematics

Abstract:
In this talk we consider linear, measure-valued transport equations on networks. The starting point of our approach is the initial and boundary value problem for the measure-valued continuity equation on a bounded interval, which - up to a parametrization - represents an arc of a network. Subsequently, we build up a global solution on the network by gluing all measures on the arcs, by means of suitable transition rules at the vertexes. Compared to standard approaches based on classical and weak solutions, the measure-theoretic framework allows one to have a better understanding of the global mass flow and some interesting related phenomena (congestion, aggregation).
In the end, we briefly discuss an example of application to the study of traffic flow on road networks.

Il seminario è parte dell'esame del corso del primo anno "Mean field games and optimal transport"

Contact person: 
Fabio Bagagiolo