Existence and uniqueness of weak solutions to the singular kernels coagulation equation with collisional breakage

TL;DR

This paper establishes the existence and uniqueness of weak solutions for a singular coagulation equation with collisional breakage, addressing unbounded kernels with singularities on axes.

Contribution

It provides new existence and uniqueness results for weak solutions to coagulation equations with singular kernels and collisional breakage.

Findings

Existence of weak solutions for unbounded, singular kernels.

Uniqueness of solutions for certain collision kernels.

Application of weak L^1 compactness method.

Abstract

In this article, we investigate the existence and uniqueness of weak solutions to the continuous coagulation equation with collisional breakage for a class of unbounded collision kernels and distribution function. The collision kernels and distribution functions may have a singularity on both the coordinate axes. The proof of the existence result is based on a classical weak L^1 compactness method applied to suitably chosen to approximate equations. The question of uniqueness is also shown for some restricted class of collision kernels.