Non-local dissipative Aw-Rascle model and its relation with Matrix-valued communication in Euler alignment

TL;DR

This paper compares a multi-dimensional Aw-Rascle model with a matrix-valued Euler-alignment system, exploring their connections across different scales and analyzing the mean-field limit under various kernel assumptions.

Contribution

It introduces a generalized Aw-Rascle model with non-local velocity offsets and examines its relation to matrix-valued communication in Euler alignment models across multiple levels.

Findings

Established connections between the models at different scales

Analyzed the mean-field limit for various kernel assumptions

Provided insights into the macroscopic and mesoscopic relations

Abstract

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 $K$.