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 ργ
n, 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 = ρ−1 n ∂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.