Global Existence and Mass Decay Analysis of solutions to the discrete Redner-Ben-Avraham-Kahng coagulation model

TL;DR

This paper proves the global existence of solutions for the discrete RBK coagulation model and shows that particle mass decays to zero over time, even with infinite initial mass, highlighting the role of large particles in creating small ones.

Contribution

It establishes the global existence of solutions for a broad class of kernels and analyzes mass decay, including cases with infinite initial mass.

Findings

Solutions exist globally for various kernels.

Mass decays to zero over time.

Large particles contribute to small particle formation.

Abstract

The Redner-Ben-Avraham-Kahng (RBK) coagulation model provide a fundamental framework for modeling the aggregation of particles in various physical and biological systems. In this paper, we investigate the global existence of solutions to the discrete version of RBK coagulation equations, encompassing a wide range of coagulation kernels. Furthermore, we demonstrate that the mass decays with time and will eventually reach to zero even if the original mass is not finite. A small size particle is produced in the RBK coagulation model when two large particles collide with a slight size difference. Dealing with the role played by large size particles in the creation of small size particles was the major challenge of this research.