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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.05140 |
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| _version_ | 1866929454306033664 |
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| author | Camilli, Fabio Festa, Adriano Marzufero, Luciano |
| author_facet | Camilli, Fabio Festa, Adriano Marzufero, Luciano |
| contents | We study a mathematical model to describe the evolution of a city, which is determined by the interaction of two large populations of agents, workers and firms. The map of the city is described by a network with the edges representing at the same time residential areas and communication routes. The two populations compete for space while interacting through the labour market. The resulting model is described by a two population Mean-Field Game system coupled with an Optimal Transport problem.We prove existence and uniqueness of the solution and we provide several numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05140 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A network model for urban planning Camilli, Fabio Festa, Adriano Marzufero, Luciano Optimization and Control 91A16, 49Q22, 35R02, 49N80 We study a mathematical model to describe the evolution of a city, which is determined by the interaction of two large populations of agents, workers and firms. The map of the city is described by a network with the edges representing at the same time residential areas and communication routes. The two populations compete for space while interacting through the labour market. The resulting model is described by a two population Mean-Field Game system coupled with an Optimal Transport problem.We prove existence and uniqueness of the solution and we provide several numerical simulations. |
| title | A network model for urban planning |
| topic | Optimization and Control 91A16, 49Q22, 35R02, 49N80 |
| url | https://arxiv.org/abs/2408.05140 |