  Dust grains are classically thought to form in the winds of AGB stars.
However, nowadays there is increasing evidence for dust formation in SNe. In
order to establish the relative importance of these two classes of stellar
sources of dust it is important to know what is the fraction of freshly formed
dust in SN ejecta that is able to survive the passage of the reverse shock and
be injected in the interstellar medium. With this aim, we have developed a new
code, GRASH_Rev, that allows to follow the dynamics of dust grains in the
shocked SN ejecta and to compute the time evolution of the mass, composition
and size distribution of the grains. We consider four well studied SNe in the
Milky Way and LMC: SN 1987a, Cas A, the Crab Nebula, and N49. For all the
simulated models, we find good agreement with observations. Our study suggests
that SN 1987A is too young for the reverse shock to have affected the dust
mass. Conversely, in the other three SNe, the reverse shock has already
destroyed between 10 and 40% of the initial dust mass. However, the largest
dust mass destruction is predicted to occur between 10^3 and 10^5 yr after the
explosions. Since the oldest SN in the sample has an estimated age of 4800 yr,
current observations can only provide an upper limit to the mass of SN dust
that will enrich the interstellar medium, the so-called effective dust yields.
We find that only between 1 and 8% of the currently observed mass will survive.
This is in good agreement with the values adopted in chemical evolution models
which consider the effect of the SN reverse shock. We discuss the astrophysical
implications of our results for dust enrichment in local galaxies and at high
redshift.
