A continuum individual based model of fragmentation: dynamics of correlation functions

TL;DR

This paper introduces a continuum individual-based model for particle fragmentation dynamics, analyzing the evolution of correlation functions in an infinite particle system, and proves existence and uniqueness of solutions.

Contribution

It develops a novel mathematical framework for modeling particle fragmentation using correlation functions in an infinite system setting.

Findings

Proved existence of solutions for the correlation function evolution equations.

Established uniqueness of these solutions.

Provided a rigorous mathematical foundation for the model.

Abstract

An individual-based model of an infinite system of point particles in $\mathbb{R}^d$ is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for this model is the set $\Gamma$ of all locally finite subsets of $\mathbb{R}^d$. The system's states are probability measures on $\Gamma$ the Markov evolution of which is described in terms of their correlation functions in a scale of Banach spaces. The existence and uniqueness of solutions of the corresponding evolution equation are proved.