Weak solutions to the continuous coagulation equation with multiple fragmentation

TL;DR

This paper proves the existence of weak solutions for the continuous coagulation equation with multiple fragmentation, even with unbounded and singular kernels, extending previous results that required boundedness or no singularity.

Contribution

It extends the existence theory to cases with unbounded and singular kernels, broadening the applicability of coagulation-fragmentation models.

Findings

Existence of weak solutions for unbounded kernels.

Handles singularities at the origin in fragmentation kernels.

Generalizes previous bounded kernel results.

Abstract

The existence of weak solutions to the continuous coagulation equation with multiple fragmentation is shown for a class of unbounded coagulation and fragmentation kernels, the fragmentation kernel having possibly a singularity at the origin. This result extends previous ones where either boundedness of the coagulation kernel or no singularity at the origin for the fragmentation kernel were assumed.