Mass conservation and gelation for the Smoluchowski coagulation equation: a generalized moment approach

TL;DR

This paper rigorously analyzes mass conservation and gelation phenomena in the Smoluchowski coagulation equation using a generalized moment approach, providing sharp conditions based on initial data and kernel properties.

Contribution

It introduces a generalized moment framework to derive precise conditions for mass conservation and gelation in the SCE with inhomogeneous kernels.

Findings

Sharp conditions for mass conservation derived

Criteria for gelation onset established

Framework applicable to various coagulation kernels

Abstract

The Smoluchowski coagulation equation (SCE) is a population balance model that describes the time evolution of cluster size distributions resulting from particle aggregation. Although it is formally a mass-conserving system, solutions may exhibit a gelation phenomenon-a sudden loss of mass-when the coagulation kernel grows superlinearly. In this paper, we rigorously analyze mass conservation and gelation for weak solutions to the SCE with inhomogeneous coagulation kernels. By introducing a generalized moment framework, we derive sharp sufficient conditions for both mass conservation and gelation, expressed in terms of the initial data and the properties of the coagulation kernel.