  We prove nonuniqueness of weak solutions to multi-dimensional generalisation
of the Aw-Rascle model of vehicular traffic. Our generalisation includes the
velocity offset in a form of gradient of density function, which results in a
dissipation effect, similar to viscous dissipation in the compressible viscous
fluid models. We show that despite this dissipation, the extension of the
method of convex integration can be applied to generate infinitely many weak
solutions connecting arbitrary initial and final states. We also show that for
certain choice of data, ill posedness holds in the class of admissible weak
solutions.

Analysis of PDEs