关键词: Cauchy problem, global solution, universe fireworks

Abstract:

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 article leads rather theoretically to an understanding of how to construct contractive mappings in a Banach space for the proof of the existence and uniqueness of the solution  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.

Key words: Cauchy problem, global solution, universe fireworks