On large time behavior and selection principle for a diffusive Carr-Penrose Model

TL;DR

This paper investigates how diffusion influences the long-term behavior of a modified LSW model, demonstrating a selection principle that determines the dominant self-similar solution and providing bounds on coarsening rates.

Contribution

It rigorously establishes a selection principle for a diffusive perturbation of the LSW model and analyzes coarsening rates in the full diffusive model.

Findings

Selection principle identified for the diffusive LSW model.

Upper bounds on coarsening rates derived.

Self-similar solutions are singled out by diffusion.

Abstract

This paper is concerned with the study of a diffusive perturbation of the linear LSW model introduced by Carr and Penrose. A main subject of interest is to understand how the presence of diffusion acts as a selection principle, which singles out a particular self-similar solution of the linear LSW model as determining the large time behavior of the diffusive model. A selection principle is rigorously proven for a model which is a semi-classical approximation to the diffusive model. Upper bounds on the rate of coarsening are also obtained for the full diffusive model.