A granular model for crowd motion and pedestrian flow
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866918016269156352 |
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| author | Igbida, Noureddine Urbano, José Miguel |
| author_facet | Igbida, Noureddine Urbano, José Miguel |
| contents | 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 variational solution of the congested crowd motion problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17361 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A granular model for crowd motion and pedestrian flow Igbida, Noureddine Urbano, José Miguel Analysis of PDEs 76A30, 35K65, 35B40 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 variational solution of the congested crowd motion problem. |
| title | A granular model for crowd motion and pedestrian flow |
| topic | Analysis of PDEs 76A30, 35K65, 35B40 |
| url | https://arxiv.org/abs/2402.17361 |