Mass-conserving weak solutions to the coagulation and collisional breakage equation with singular rates

TL;DR

This paper proves the existence of mass-conserving weak solutions for a coagulation and breakage equation with singular kernels, using truncation methods and weak L1 compactness.

Contribution

It introduces a novel approach to establish existence of solutions with singular kernels in coagulation-breakage models.

Findings

Existence of mass-conserving solutions is proven.

Solutions accommodate singularities near the origin.

Method applies to continuous coagulation and breakage equations.

Abstract

In this article, the existence of mass-conserving solutions is investigated to the continuous coagulation and collisional breakage equation with singular coagulation kernels. Here, the probability distribution function attains singularity near the origin. The existence result is constructed by using both conservative and non-conservative truncations to the continuous coagulation and collisional breakage equation. The proof of the existence result relies on a classical weak L1 compactness method.