The singular kernel coagulation equation with multifragmentation

TL;DR

This paper proves the existence of solutions to a singular coagulation equation with multifragmentation, using weighted spaces and compactness methods, and also provides a uniqueness result.

Contribution

It introduces a new approach to establish existence and uniqueness of solutions for the singular coagulation equation with multifragmentation.

Findings

Existence of solutions in weighted L^1 spaces.

Application of weak L^1 compactness methods.

Uniqueness results under certain conditions.

Abstract

In this article we prove the existence of solutions to the singular coagulation equation with multifragmentation. We use weighted $L^1$-spaces to deal with the singularities and to obtain regular solutions. The Smoluchowski kernel is covered by our proof. The weak $L^1$ compactness methods are applied to suitably chosen approximating equations as a base of our proof. A more restrictive uniqueness result is also given.