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PDEs & Applications Seminar

Friday, February 28, 2025

Time: 10:30 a.m.  Place: Jeffery Hall, Room 319

Speaker: Massimiliano Rosini (Uniwersytet Marii Curie-Sklodowskiej & Universita' “G. d’Annunzio” di Chieti-Pescara)

Title: Micro and macro descriptions of traffic

Abstract: We will explore the interplay between deterministic particle systems and one-dimensional conservation laws, with applications to vehicular traffic models and pedestrian flows.

We begin by discussing follow-the-leader dynamics, described by systems of ordinary differential equations, and show how they can approximate solutions of conservation laws. The talk focuses on the Cauchy problem for the Lighthill-Whitham-Richards (LWR) traffic model and extends to initial-boundary value problems, highlighting its adaptability to diverse traffic scenarios.The seminar also examines the Aw-Rascle-Zhang (ARZ) traffic model, which generalizes the LWR framework to account for multi-population dynamics, and the Hughes model for pedestrian flow, which incorporates decision-making processes such as exit selection. This presentation demonstrates how deterministic particle systems enhance our understanding of macroscopic models in traffic and pedestrian dynamics, offering valuable insights into complex real-world phenomena.

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