Asymptotic Stability of the Landau-Lifshitz Equation

TL;DR

This paper proves the asymptotic stability of equilibrium points in the Landau-Lifshitz equation, which models magnetic domains in ferromagnetic materials, using a Lyapunov function to ensure data stability in magnetic storage.

Contribution

It establishes the asymptotic stability of the Landau-Lifshitz equation's equilibrium points with a novel Lyapunov function approach.

Findings

Proves asymptotic stability of magnetic domain equilibria

Introduces a Lyapunov function for stability analysis

Supports stable data storage in ferromagnetic structures

Abstract

The Landau--Lifshitz equation describes the behaviour of magnetic domains in ferromagnetic structures. Recently such structures have been found to be favourable for storing digital data. Stability of magnetic domains is important for this. Consequently, asymptotic stability of the equilibrium points in the Landau--Lifshitz equation are established. A suitable Lyapunov function is presented.