Hysteresis for ferromagnetism: asymptotics of some 2-scale Landau-Lifshitz model

Hysteresis for ferromagnetism: asymptotics of some two-scale Landau-Lifshitz model

Quasi-stationary Limit and a Landau-lifshitz Equation in Ferromagnetism

In this paper we study a Landau-Lifshitz equation in ferromagnetism without exchange energy as a quasi-stationary limit of a coupled Maxwell system as dielectric permittivity approaches zero. We present a different formulation and proof of this quasi-stationary limit result. We also prove a new uniqueness and stability result for the limit Landau-Lifshitz equation.

Asymptotic Stability , Concentration , and Oscillation in Harmonic Map Heat - Flow , Landau - Lifshitz , and Schrödinger Maps on R 2

We consider the Landau-Lifshitz equations of ferromagnetism (including the harmonic map heat-flow and Schrödinger flow as special cases) for degree m equivariant maps from R2 to S2. If m ≥ 3, we prove that near-minimal energy solutions converge to a harmonic map as t → ∞ (asymptotic stability), extending previous work (Gustafson et al., Duke Math J 145(3), 537–583, 2008) down to degree m = 3. D...

A pr 2 00 9 ASYMPTOTIC STABILITY , CONCENTRATION , AND OSCILLATION IN HARMONIC MAP HEAT - FLOW , LANDAU - LIFSHITZ

We consider the Landau-Lifshitz equations of ferromagnetism (including the harmonic map heat-flow and Schrödinger flow as special cases) for degree m equivariant maps from R to S. If m ≥ 3, we prove that near-minimal energy solutions converge to a harmonic map as t → ∞ (asymptotic stability), extending previous work [11] down to degree m = 3. Due to slow spatial decay of the harmonic map compon...

On Landau-lifshitz Equations of No-exchange Energy Models in Ferromagnetics

In this paper, we study Landau-Lifshitz equations of ferromagnetism with a total energy that does not include a so-called exchange energy. Many problems, including existence, stability, regularity and asymptotic behaviors, have been extensively studied for such equations of models with the exchange energy. Problems turn out quite different and challenging for Landau-Lifshitz equations of no-exc...