Asymptotic Stability of the Landau-Lifshitz Equation

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.