  We prove existence and uniqueness of the global solution to the Cauchy
problem on a universe fireworks model with finite total mass at the initial
state when the ratio of the mass surviving the explosion, the probability of
the explosion of fragments and the probability function of the velocity change
of a surviving particle satisfy the corresponding physical conditions. Although
the nonrelativistic Boltzmann-like equation modeling the universe fireworks is
mathematically easy, this paper leads rather theoretically to an understanding
of how to construct contractive mappings in a Banach space for the proof of the
existence and uniqueness by means of methods taken from the famous work by
DiPerna & Lions about the Boltzmann equation. We also show both the regularity
and the time-asymptotic behavior of solution to the Cauchy problem.
