On a diffusive version of the Lifschitz-Slyozov-Wagner equation

TL;DR

This paper introduces a diffusive variant of the Lifschitz-Slyozov-Wagner equations derived from the Becker-Döring system, proves their mathematical properties, and shows convergence to classical solutions as diffusion vanishes.

Contribution

It develops a diffusive version of the LSW equations, establishes existence and uniqueness, and demonstrates convergence to classical solutions in the zero diffusion limit.

Findings

Existence and uniqueness of solutions for the diffusive LSW system.

Convergence of diffusive solutions to classical LSW solutions as diffusion approaches zero.

The coarsening rate of the diffusive system converges to that of the classical system.

Abstract

This paper is concerned with the Becker-D\"{o}ring (BD) system of equations and their relationship to the Lifschitz-Slyozov-Wagner (LSW) equations. A diffusive version of the LSW equations is derived from the BD equations. Existence and uniqueness theorems for this diffusive LSW system are proved. The major part of the paper is taken up with proving that solutions of the diffusive LSW system converge in the zero diffusion limit to solutions of the classical LSW system. In particular, it is shown that the rate of coarsening for the diffusive system converges to the rate of coarsening for the classical system.