  Supernova generated shock waves are responsible for most of the destruction
of dust grains in the interstellar medium (ISM). Calculations of the dust
destruction timescale have so far been carried out using plane parallel steady
shocks, however that approximation breaks down when the destruction timescale
becomes longer than that for the evolution of the supernova remnant (SNR)
shock. In this paper we present new calculations of grain destruction in
evolving, radiative SNRs. To facilitate comparison with the previous study by
Jones et al. (1996), we adopt the same dust properties as in that paper. We
find that the efficiencies of grain destruction are most divergent from those
for a steady shock when the thermal history of a shocked gas parcel in the SNR
differs significantly from that behind a steady shock. This occurs in shocks
with velocities >~ 200 km/s for which the remnant is just beginning to go
radiative. Assuming SNRs evolve in a warm phase dominated ISM, we find dust
destruction timescales are increased by a factor of ~2 compared to those of
Jones et al. (1996), who assumed a hot gas dominated ISM. Recent estimates of
supernova rates and ISM mass lead to another factor of ~3 increase in the
destruction timescales, resulting in a silicate grain destruction timescale of
~2-3 Gyr. These increases, while not able resolve the problem of the discrepant
timescales for silicate grain destruction and creation, are an important step
towards understanding the origin, and evolution of dust in the ISM.
