Bounds on coarsening rates for the Lifschitz-Slyozov-Wagner equation

TL;DR

This paper establishes point-wise in time upper and lower bounds on the coarsening rates of solutions to the Lifschitz-Slyozov-Wagner equation, enhancing understanding of its long-term behavior for general initial data.

Contribution

It provides new point-wise bounds on coarsening rates for the LSW system, complementing previous time-averaged and near-self-similar results.

Findings

Derived point-wise bounds on coarsening rates

Extended understanding to general initial data

Complemented existing bounds by Dai, Pego, Niethammer, and Velasquez

Abstract

This paper is concerned with the large time behavior of solutions to the Lifschitz-Slyozov-Wagner (LSW) system of equations. Point-wise in time upper and lower bounds on the rate of coarsening are obtained for solutions with fairly general initial data. These bounds complement the time averaged upper bounds obtained by Dai and Pego, and the point-wise in time upper and lower bounds obtained by Niethammer and Velasquez for solutions with initial data close to a self-similar solution.