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

Abstract

We compare the multidimensional 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 microscopic, mesoscopic, and macroscopic (hydrodynamic) levels, and overview the results on the mean-field limit for various assumptions on $K$.