Existence of global solutions to the Cauchy problem for the inelastic Boltzmann equation with near-vacuum data

TL;DR

This paper proves the existence and uniqueness of solutions to the inelastic Boltzmann equation with small initial data near vacuum, using an iterative method, expanding understanding of kinetic equations in dilute regimes.

Contribution

It establishes the existence and uniqueness of mild and weak solutions for small data in Maxwellian spaces, applying the Kaniel-Shinbrot iteration method to inelastic collisions.

Findings

Solutions exist and are unique for small initial data

The method applies to inelastic Boltzmann equations near vacuum

The approach uses the Kaniel-Shinbrot iterative process

Abstract

The Cauchy problem for the inelastic Boltzmann equation is studied for small data. Existence and uniqueness of mild and weak solutions is obtained for sufficiently small data that lies in the space of functions bounded by Maxwellians. The technique used to derive the result is the well known iteration process of Kaniel and Shinbrot.