Global classical solutions to the continuous coagulation equation with collisional breakage

TL;DR

This paper proves the existence and uniqueness of mass-conserving classical solutions for the continuous coagulation equation with collisional breakage, even allowing for singularities at the origin, using the compactness method.

Contribution

It establishes the first comprehensive existence and uniqueness results for this class of coagulation equations with singular distribution functions.

Findings

Existence of mass-conserving classical solutions

Uniqueness of the solutions

Solutions may have singularities at the origin

Abstract

Existence and uniqueness of mass-conserving classical solutions to the continuous coagulation equation with collisional breakage are investigated for an unbounded class of collision kernels and a particular case of the distribution function. The distribution function may have a possibility to attain singularity at the origin. The proof of the existence result relies on the compactness method. Moreover, a uniqueness result is shown. In addition, it is observed that the uniqueness solution is mass-conserving.