On Global Asymptotic Stability for the LSW Model with subcritical initial data

TL;DR

This paper proves that solutions to the LSW model with subcritical initial data globally stabilize over time, extending previous local stability results using a novel approach applicable to complex infinite-dimensional systems.

Contribution

It establishes a global asymptotic stability result for the LSW system, advancing understanding beyond prior local stability findings and employing a method suitable for systems lacking Lyapunov functions.

Findings

Solutions converge to equilibrium globally

Extends local stability to global stability for the LSW model

Applicable to infinite-dimensional dynamical systems

Abstract

The main result of the paper is a global asymptotic stability result for solutions to the Lifschitz-Slyozov-Wagner (LSW) system of equations. This extends some local asymptotic stability results of Niethammer-Vel\'{a}zquez (2006). The method of proof is along similar lines to the one used in a previous paper of the authors. This previous paper proves global asymptotic stability for a class of infinite dimensional dynamical systems for which no Lyapounov function is (apparently) available.