A note on mass-conserving solutions to the coagulation-fragmentation equation by using non-conservative approximation

TL;DR

This paper demonstrates that non-conservative approximations of coagulation-fragmentation equations can produce mass-conserving solutions, even in cases where gelation might occur, expanding understanding of solution behavior.

Contribution

It shows that non-conservative approximations can yield mass-conserving solutions for broad classes of kernels, contrary to typical expectations.

Findings

Non-conservative approximation can produce mass-conserving solutions

Mass conservation holds for large classes of unbounded kernels

Implications for understanding gelation phenomena

Abstract

In general, the non-conservative approximation of coagulation-fragmentation equations (CFEs) may lead to the occurrence of gelation phenomenon. In this article, it is shown that the non-conservative approximation of CFEs can also provide the existence of mass conserving solutions to CFEs for large classes of unbounded coagulation and fragmentation kernels.