  We consider sputtering of dust grains, believed to be formed in cooling
supernovae ejecta, under the influence of reverse shocks. In the regime of
self-similar evolution of reverse shocks, we can follow the evolution of ejecta
density and temperature analytically as a function of time in different parts
of the ejecta, and calculate the sputtering rate of graphite and silicate
grains embedded in the ejecta as they encounter the reverse shock. Through
analytic (1D) calculations, we find that a fraction of dust mass ($
1\hbox{--}20$% for silicates and %$\le 5$% for graphites) can be sputtered by
reverse shocks, the fraction varying with the grain size distribution and the
steepness of the density profile of the ejecta mass. It is expected that many
more grains will get sputtered in the region between the forward and reverse
shocks, so that our analytical results provide a lower limit to the destroyed
fraction of dust mass.
