Non-local dissipative Aw-Rascle model and its relation with Matrix-valued communication in Euler alignment
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912024143855616 |
|---|---|
| author | Chaudhuri, Nilasis Peszek, Jan Szlenk, Maja Zatorska, Ewelina |
| author_facet | Chaudhuri, Nilasis Peszek, Jan Szlenk, Maja Zatorska, Ewelina |
| contents | We compare the multi-dimensional generalisation of the Aw-Rascle model with the pressureless Euler-alignment system, in which the communication weight is matrix-valued. Our generalisation includes the velocity offset in the form of a gradient of a non-local density function, given by the convolution with a kernel $K$. We investigate connections between these models at the macroscopic, mesoscopic and macroscopic (hydrodynamic) level, and overview the results on the mean-field limit for various assumptions on $K$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07593 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-local dissipative Aw-Rascle model and its relation with Matrix-valued communication in Euler alignment Chaudhuri, Nilasis Peszek, Jan Szlenk, Maja Zatorska, Ewelina Analysis of PDEs We compare the multi-dimensional generalisation of the Aw-Rascle model with the pressureless Euler-alignment system, in which the communication weight is matrix-valued. Our generalisation includes the velocity offset in the form of a gradient of a non-local density function, given by the convolution with a kernel $K$. We investigate connections between these models at the macroscopic, mesoscopic and macroscopic (hydrodynamic) level, and overview the results on the mean-field limit for various assumptions on $K$. |
| title | Non-local dissipative Aw-Rascle model and its relation with Matrix-valued communication in Euler alignment |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.07593 |