The Discrete Unbounded Coagulation-Fragmentation Equation with Growth, Decay and Sedimentation

TL;DR

This paper investigates a generalized discrete coagulation-fragmentation model incorporating growth, decay, and sedimentation, establishing existence and uniqueness of solutions under weaker conditions and supporting findings with numerical simulations.

Contribution

It extends previous models by including additional processes and relaxes assumptions, providing new theoretical results and numerical validation.

Findings

Existence of classical global solutions under strong linear processes

Uniqueness of solutions in the generalized model

Numerical simulations support theoretical conclusions

Abstract

In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong. This paper extends several previous results both by considering a more general model and and also signnificantly weakening the assumptions. Theoretical conclusions are supported by numerical simulations.