  Outflows of young stars drive shocks into dusty, molecular regions. Most
models of such shocks assume that they are steady and propagating perpendicular
to the magnetic field. Real shocks often violate both of these assumptions and
the media through which they propagate are inhomogeneous. We use the code
employed previously to produce the first time-dependent simulations of
fast-mode, oblique C-type shocks interacting with density perturbations. We
include a self-consistent calculation of the thermal and ionisation balances
and a fluid treatment of grains. We identify features that develop when a
multifluid shock encounters a density inhomogeneity to investigate whether any
part of the precursor region ever behaves in a quasi-steady fashion. If it does
the shock may be modelled approximately without solving the time-dependent
hydromagnetic equations. Simulations were made for initially steady oblique
C-type shocks encountering density inhomogeneities. For a semi-finite
inhomogeneity with a density larger than the surrounding medium, a transmitted
shock evolves from being J-type to a steady C-type shock on a timescale
comparable to the ion-flow time through it. A sufficiently upstream part of the
precursor of an evolving J-type shock is quasi-steady. The ion-flow timescale
is also relevant for the evolution of a shock moving into a region of
decreasing density. The models for shocks propagating into regions in which the
density increases and then decreases to its initial value cannot be entirely
described in terms of the results obtained for monotonically increasing and
decreasing densities. For the latter model, the long-term evolution to a C-type
shock cannot be approximated by quasi-steady models.
