Time-Evolving Measures and Macroscopic Modeling of Pedestrian Flow

Benedetto Piccoli, Andrea Tosin

Research output: Contribution to journalArticlepeer-review

108 Scopus citations


This paper introduces a new model of pedestrian flow, formulated within a measure-theoretic framework. It consists of a macroscopic representation of the system via a family of measures which, pushed forward by some flow maps, provide an estimate of the space occupancy by pedestrians at successive times. From the modeling point of view, this setting is particularly suitable for treating nonlocal interactions among pedestrians, obstacles, and wall boundary conditions. In addition, the analysis and numerical approximation of the resulting mathematical structures, which are the principal objectives of this work, follow more easily than for models based on standard hyperbolic conservation laws.

Original languageEnglish (US)
Pages (from-to)707-738
Number of pages32
JournalArchive For Rational Mechanics And Analysis
Issue number3
StatePublished - Mar 2011

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Analysis
  • Mathematics (miscellaneous)


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