  Supernovae (SN) explosions are thought to be an important source of dust in
galaxies. At the same time strong shocks from SNe are known as an efficient
mechanism of dust destruction via thermal and kinetic sputtering. A critically
important question of how these two hypotheses of SNe activity control the dust
budget in galaxies is still not quite clearly understood. In this paper we
address this question within 3D multi-fluid hydrodynamical simulations,
treating separately the SNe injected dust and the dust pre-existed in ambient
interstellar gas. We focus primarily on how the injected and the pre-existing
dust is destroyed by shock waves and hot gas in the SN bubble depending on the
density of ambient gas. Within our model we estimate an upper limit of the
SN-produced dust mass which can be supplied into interstellar medium. For a SN
progenitor mass of 30 $M_\odot$ and the ejected dust mass $M_d=1~M_\odot$ we
constrain the dust mass that can be delivered into the ISM as $\geq
0.13~M_\odot$, provided that the SN has injected large dust particles with
$a\geq 0.1~\mu$m.
