Spatial coagulation with bounded coagulation rate

TL;DR

This paper proves the well-posedness of the spatial coagulation equation with bounded coagulation rate under certain conditions on the convection term, including multiple coagulation, fragmentation, and scattering effects.

Contribution

It establishes the well-posedness of the spatial coagulation equation with bounded rates for a broad class of kernels, considering complex particle interactions.

Findings

Proves well-posedness for all times under specified conditions.

Includes analysis of multiple coagulation, fragmentation, and scattering.

Provides conditions on the convection term for stability.

Abstract

We prove that the spatial coagulation equation with bounded coagulation rate is well-posed for all times in a given class of kernels if the convection term of the underlying particle dynamics has divergence bounded below by a positive constant. Multiple coagulations, fragmentation and scattering are also considered.