  We present a theoretical and numerical study of the self-steepening and shock
formation of large-amplitude dust ion-acoustic waves (DIAWs) in dusty plasmas.
We compare the non-dispersive two fluid model, which predicts the formation of
large amplitude compressive and rarefactive dust ion-acoustic (DIA) shocks,
with Vlasov/fluid simulations where ions are treated kinetically while a
Boltzmann distribution is assumed for the electrons.
