Weak solutions to the continuous coagulation model with collisional breakage

TL;DR

This paper proves the existence of weak solutions for a continuous coagulation model with collisional breakage, accounting for complex particle interactions and potential singularities in particle size distribution.

Contribution

It establishes a global existence theorem for weak solutions under unbounded collision kernels and distribution functions, advancing the mathematical understanding of particle coagulation and breakage.

Findings

Proves global existence of weak solutions.

Handles unbounded collision kernels and distribution functions.

Addresses algebraic singularities in particle size distribution.

Abstract

A global existence theorem on weak solutions is shown for the continuous coagulation equation with collisional breakage under certain classes of unbounded collision kernels and distribution functions. This model describes the dynamics of particle growth when binary collisions occur to form either a single particle via coalescence or two/more particles via breakup with possible transfer of mass. Each of these processes may take place with a suitably assigned probability depending on the volume of particles participating in the collision. The distribution function may have a possibility to attain an algebraic singularity for small volumes.