Growth--fragmentation--coagulation equations with unbounded coagulation kernels

TL;DR

This paper proves the global existence of solutions for a complex growth--fragmentation--coagulation equation with unbounded kernels, using advanced regularization techniques to handle large cluster growth.

Contribution

It establishes the first global solvability results for such equations with unbounded coagulation kernels in high-moment function spaces.

Findings

Proves global in time solvability of the equation

Uses moment regularization of the semigroup

Handles unbounded coagulation kernels

Abstract

In this paper we prove the global in time solvability of the continuous growth--fragmentation--coagulation equation with unbounded coagulation kernels, in spaces of functions having finite moments of sufficiently high order. The main tool is the recently established result on moment regularization of the linear growth--fragmentation semigroup that allows us to consider coagulation kernels whose growth for large clusters is controlled by how good the regularization is, in a similar manner to the case when the semigroup is analytic.