Pith. sign in

REVIEW 1 cited by

A Class of Non-Local Models for Pedestrian Traffic

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1104.2985 v2 pith:2PULPDPY submitted 2011-04-15 math.AP

Rinaldo M. Colombo , Mauro Garavello (DISTA) , Magali Lécureux-Mercier (MAPMO) This is my paper · ORCID
classification math.AP
keywords classmodelscrowdequationpedestrianpropertiesqualitativeaccording
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move towards a fixed target, deviating from the best path according to the instantaneous crowd distribution. The resulting equation is a conservation law with a nonlocal flux. Each equation in this class generates a Lipschitz semigroup of solutions and is stable with respect to the functions and parameters defining it. Moreover, key qualitative properties such as the boundedness of the crowd density are proved. Specific models are presented and their qualitative properties are shown through numerical integrations.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The Cauchy Problem for Symmetric Hyperbolic Systems with Nonlocal Potentials

    math.AP 2025-07 conditional novelty 7.0 of 10

    Under smallness and decay conditions on nonlocal potentials, symmetric hyperbolic systems on curved spacetimes admit strong solutions to the Cauchy problem, with a sharp threshold beyond which solutions fail.

Pith tools