Convergence of the discrete Redner-Ben-Avraham-Kahng coagulation equation

TL;DR

This paper investigates the relationship between discrete and continuous RBK coagulation models, proving convergence of the discrete model to the continuous one using stability and compactness techniques.

Contribution

It establishes the convergence of discrete RBK models to the continuous model, providing a rigorous link between the two formulations.

Findings

Discrete models converge to the continuous RBK model.

Weak stability and compactness are key to the convergence proof.

A priori estimates facilitate the analysis of the models.

Abstract

This article looks at the relationship between the discrete and the continuous Redner-Ben-Avraham-Kahng (RBK) coagulation models. On the basis of a priori estimation, a weak stability principle and the weak compactness in $L_1$ for the continuous RBK model is shown. By employing a sequence of discrete models to approximate the continuous one, we show that how discrete model eventually converges to the the modified continuous one using the stability principle.