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Transient evolution of C-type shocks in dusty regions of varying density

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.