# The Lifshitz-Slyozov-Wagner equation for reaction-controlled kinetics

## TL;DR

This paper rigorously derives a weak form of the Lifshitz-Slyozov-Wagner equation from a Stefan-type problem, establishing its validity in reaction-controlled coarsening and in the limit of low particle surface-area density.

## Contribution

It provides a rigorous derivation of the Lifshitz-Slyozov-Wagner equation as a homogenization limit for reaction-controlled coarsening processes.

## Key findings

- The weak form of the Lifshitz-Slyozov-Wagner equation is derived rigorously.
- The effective mean-field description is valid in the limit of vanishing particle surface-area density.
- The derivation connects microscopic Stefan-type problems to macroscopic coarsening equations.

## Abstract

We rigorously derive a weak form of the Lifshitz-Slyozov-Wagner equation as the homogenization limit of a Stefan-type problem describing reaction-controlled coarsening of a large number of small spherical particles. Moreover, we deduce that the effective mean-field description holds true in the particular limit of vanishing surface-area density of particles.