A granular model for crowd motion and pedestrian flow
Abstract
We study a granular model for congested crowd motion and pedestrian flow. Our approach is based on an approximation through a Hele-Shaw type equation involving a degenerate operator of $p$-Laplacian type and a linear drift, for which we prove existence and uniqueness using nonlinear semigroup methods and the doubling variables technique. Our main result shows that, as $p \to \infty$, the weak solutions of the $p-$problem converge to a solution of the congested crowd motion problem.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2024
- DOI:
- 10.48550/arXiv.2402.17361
- arXiv:
- arXiv:2402.17361
- Bibcode:
- 2024arXiv240217361I
- Keywords:
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- Mathematics - Analysis of PDEs;
- 76A30;
- 35K65;
- 35B40