Convergence of rough follow-the-leader approximations and existence of weak solutions for the one-dimensional Hughes model.

We prove that rough Follow-the-Leader (FtL) approximations are compact in the strong $ L^1 $–topology, with a compensated compactness argument. We then apply this result to prove the existence of a weak solution of the one-dimensional Hughes model. Here, we consider general initial data $ \rho_0 \in L^\infty $ and general costs $ c \in W^{1, \infty} $. We also investigate the ill-posedness of the FtL–Hughes model, and how the ill-posedness issues affect numerical simulations. [ABSTRACT FROM AUTHOR]