Surface density profiles of gas (red) and dust (blue) at different times (solid lines). The initial condition corresponds to the self-similar profile (dashed lines). Top: simulation initially behaves in the same way as the power law profile until 0.1 Myr. Mid: at 0.4 Myr the dust supply gets exhausted before the back-reaction push can further deplete the gaseous disk. Bottom: after 1 Myr, the gas profile looks very similar to its initial condition, but most of the dust has been accreted.