Hard congestion limit of the dissipative Aw-Rascle system with a polynomial offset function

Abstract

We study the Aw-Rascle system in a one-dimensional domain with periodic boundary conditions, where the offset function is replaced by the gradient of the function ρnγ, where γ→∞. The resulting system resembles the 1D pressureless compressible Navier-Stokes system with a vanishing viscosity coefficient in the momentum equation and can be used to model traffic and suspension flows. We first prove the existence of a unique global-in-time classical solution for fixed n. Unlike the previous result for this system, we obtain global existence without needing to add any approximation terms to the system. This is by virtue of a n-uniform lower bound on the density which is attained by carrying out a maximum-principle argument on a suitable potential, Wn=ρn−1∂xwn. Then we prove the convergence to a weak solution of a hybrid free-congested system as n→∞, which is known as the hard-congestion model.