Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic
We consider the follow-the-leader approximation of the Aw-Rascle-Zhang (ARZ) model for traffic flow in a multi population formulation. We prove rigorous convergence to weak solutions of the ARZ system in the many particle limit in presence of vacuum. The result is based on uniform ${\mathbf{BV}}$...
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| Format: | Article |
| Language: | English |
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AIMS Press
2017-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017009 |
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| _version_ | 1832590084335992832 |
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| author | Marco Di Francesco Simone Fagioli Massimiliano D. Rosini |
| author_facet | Marco Di Francesco Simone Fagioli Massimiliano D. Rosini |
| author_sort | Marco Di Francesco |
| collection | DOAJ |
| description | We consider the follow-the-leader approximation of the Aw-Rascle-Zhang (ARZ) model for traffic flow in a multi population formulation. We prove rigorous convergence to weak solutions of the ARZ system in the many particle limit in presence of vacuum. The result is based on uniform ${\mathbf{BV}}$ estimates on the discrete particle velocity. We complement our result with numerical simulations of the particle method compared with some exact solutions to the Riemann problem of the ARZ system. |
| format | Article |
| id | doaj-art-de63617bf7f8431db5e0c5e70abcdb9b |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-de63617bf7f8431db5e0c5e70abcdb9b2025-01-24T02:39:32ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-01-0114112714110.3934/mbe.2017009Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular trafficMarco Di Francesco0Simone Fagioli1Massimiliano D. Rosini2DISIM, Università degli Studi dell'Aquila, via Vetoio 1 (Coppito), 67100 LAquila (AQ), ItalyDISIM, Università degli Studi dell'Aquila, via Vetoio 1 (Coppito), 67100 LAquila (AQ), ItalyInstytut Matematyki, Uniwersytet Marii Curie-Skłodowskiej, pl. Marii Curie-Sk lodowskiej 1, 20-031 Lublin, PolandWe consider the follow-the-leader approximation of the Aw-Rascle-Zhang (ARZ) model for traffic flow in a multi population formulation. We prove rigorous convergence to weak solutions of the ARZ system in the many particle limit in presence of vacuum. The result is based on uniform ${\mathbf{BV}}$ estimates on the discrete particle velocity. We complement our result with numerical simulations of the particle method compared with some exact solutions to the Riemann problem of the ARZ system.https://www.aimspress.com/article/doi/10.3934/mbe.2017009aw-rascle-zhang modelsecond order models for vehicular trafficsmany particle limit |
| spellingShingle | Marco Di Francesco Simone Fagioli Massimiliano D. Rosini Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic Mathematical Biosciences and Engineering aw-rascle-zhang model second order models for vehicular traffics many particle limit |
| title | Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic |
| title_full | Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic |
| title_fullStr | Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic |
| title_full_unstemmed | Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic |
| title_short | Many particle approximation of the Aw-Rascle-Zhang second order model for vehicular traffic |
| title_sort | many particle approximation of the aw rascle zhang second order model for vehicular traffic |
| topic | aw-rascle-zhang model second order models for vehicular traffics many particle limit |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017009 |
| work_keys_str_mv | AT marcodifrancesco manyparticleapproximationoftheawrasclezhangsecondordermodelforvehiculartraffic AT simonefagioli manyparticleapproximationoftheawrasclezhangsecondordermodelforvehiculartraffic AT massimilianodrosini manyparticleapproximationoftheawrasclezhangsecondordermodelforvehiculartraffic |