Well-posedness for a coagulation multiple-fragmentation equation

TL;DR

This paper establishes the existence and uniqueness of solutions for a coagulation-multiple fragmentation equation with certain kernels, using Wasserstein-type distances, advancing the mathematical understanding of particle systems with fragmentation and coalescence.

Contribution

It provides new results on well-posedness for a class of coagulation-fragmentation equations with possibly infinite fragmentation rates, employing Wasserstein distances.

Findings

Proved existence and uniqueness of solutions for the equation.

Extended the analysis to kernels with infinite total fragmentation rate.

Utilized Wasserstein-type distance to handle coalescence phenomena.

Abstract

We consider a coagulation multiple-fragmentation equation, which describes the concentration $c\_t(x)$ of particles of mass $x \in (0,\infty)$ at the instant $t \geq 0$ in a model where fragmentation and coalescence phenomena occur. We study the existence and uniqueness of measured-valued solutions to this equation for homogeneous-like kernels of homogeneity parameter $\lambda \in (0,1]$ and bounded fragmentation kernels, although a possibly infinite total fragmentation rate, in particular an infinite number of fragments, is considered. This work relies on the use of a Wasserstein-type distance, which has shown to be particularly well-adapted to coalescence phenomena. It was introduced in previous works on coagulation and coalescence.