Analysis of a spatio-temporal advection-diffusion model for human behaviors during a catastrophic event
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866917585227874304 |
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| author | Khalil, K. Lanza, V. Manceau, D. Aziz-Alaoui, M. A. Provitolo, D. |
| author_facet | Khalil, K. Lanza, V. Manceau, D. Aziz-Alaoui, M. A. Provitolo, D. |
| contents | In this work, using the theory of first-order macroscopic crowd models, we introduce a compartmental advection-diffusion model, describing the spatio-temporal dynamics of a population in different human behaviors (alert, panic and control) during a catastrophic event. For this model, we prove the local existence, uniqueness and regularity of a solution, as well as the positivity and $L^1$--boundedness of this solution. Then, in order to study the spatio-temporal propagation of these behavioral reactions within a population during a catastrophic event, we present several numerical simulations for different evacuation scenarios. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02520 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Analysis of a spatio-temporal advection-diffusion model for human behaviors during a catastrophic event Khalil, K. Lanza, V. Manceau, D. Aziz-Alaoui, M. A. Provitolo, D. Analysis of PDEs In this work, using the theory of first-order macroscopic crowd models, we introduce a compartmental advection-diffusion model, describing the spatio-temporal dynamics of a population in different human behaviors (alert, panic and control) during a catastrophic event. For this model, we prove the local existence, uniqueness and regularity of a solution, as well as the positivity and $L^1$--boundedness of this solution. Then, in order to study the spatio-temporal propagation of these behavioral reactions within a population during a catastrophic event, we present several numerical simulations for different evacuation scenarios. |
| title | Analysis of a spatio-temporal advection-diffusion model for human behaviors during a catastrophic event |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2301.02520 |