Analysis of the generalised Aw-Rascle model

Abstract

We consider the multi-dimensional generalization of the Aw-Rascle system for vehicular traffic. For arbitrary large class of initial data and the periodic domain, we prove the existence of globalin-time measure-valued solutions. Moreover, using the relative energy technique, we show that the measure-valued solutions coincide with the classical solutions as long as the latter exist.

Nonuniqueness of weak solutions to the dissipative Aw-Rascle model

“…Taking this form of the offset function has the advantage of dimension compatibility with the velocity vector field in higher dimensions. The existence of measure-valued solutions to such generalisation in multi-dimensional setting, and their weak-strong uniqueness was recently proved in [8].…”