  The hierarchical clustering inherent in Lambda-CDM cosmology seems to produce
many of the observed characteristics of large-scale structure. But some glaring
problems still remain, including the over-prediction (by a factor 10) of the
number of dwarf galaxies within the virialized population of the local group.
Several secondary effects have already been proposed to resolve this problem.
It is still not clear, however, whether the principal solution rests with
astrophysical processes, such as early feedback from supernovae, or possibly
with as yet undetermined properties of the dark matter itself. In this paper,
we carry out a detailed calculation of the dwarf halo evolution incorporating
the effects of a hypothesized dark-matter decay, D -> D'+l, where D is the
unstable particle, D' is the more massive daughter particle and l is the other,
lighter (or possibly massless) daughter particle. This process preferentially
heats the smaller haloes, expanding them during their evolution and reducing
their present-day circular velocity. We find that this mechanism can account
very well for the factor 4 deficit in the observed number of systems with
velocity 10--20 km/s compared to those predicted by the numerical simulations,
if dm/m_D' ~ 5-7 x 10^{-5}, where dm is the mass difference between the initial
and final states. The corresponding lifetime tau cannot be longer than ~30 Gyr,
but may be as short as just a few Gyr.
