On Classical solution to the Discrete Coagulation Equations with Collisional Breakage

TL;DR

This paper proves the existence, uniqueness, and key properties of classical solutions to discrete coagulation equations with collisional breakage, under certain conditions on the collisional kernel.

Contribution

It establishes the first rigorous existence and uniqueness results for classical solutions to these equations with linear growth kernels.

Findings

Existence of global classical solutions is proven.

Uniqueness holds under additional kernel restrictions.

Mass conservation and moment propagation are demonstrated.

Abstract

In this article, the existence of global classical solutions to the discrete coagulation equations with collisional breakage is established for collisional kernel having linear growth whereas the uniqueness is shown under additional restrictions on collisional kernel. Moreover, mass conservation property and propagation of moments of solutions are also discussed.