Open Access

  

Original research article

Asymptotic Behaviours for the Landau-Lifschitz-Bloch Equation

Author(s):

Kamel Hamdachea, Djamila Hamrounb

aLéonard de Vinci Pôle Universitaire, DVRC, 92 916 Paris La Défense Cedex, France
bLaboratoire AMNEDP, Faculté de Mathématiques, Université USTHB, B. P. 32 El Alia, Bab Ezzouar, 16111, Alger, Algérie

Advances in the Theory of Nonlinear Analysis and its Applications 3(4), 174-191.
Received: January 11, 2019

  

  

  

Accepted: October 3, 2019

  

Published: October 6, 2019

Abstract

The Landau–Lifshitz–Bloch (LLB) equation serves as an interpolation between the Bloch equation (valid at high temperatures) and the Landau–Lifshitz equation (valid at low temperatures). In this paper, we study the asymptotic behaviour of the solutions of the LLB equation as the temperature approaches infinity or zero. Interestingly, in the first case, the behaviour depends on the scaling of the damping parameter δ and the volume exchange parameter a. Three cases are examined, leading respectively to a linear stationary equation, Bloch equation, or Stokes equation. For small temperature behaviour, with δ and a independent of temperature, it is shown that the limit of the LLB equation coincides with the Landau–Lifshitz–Gilbert equation.

Keywords: Landau–Lifshitz–Bloch equation, Landau–Lifshitz–Gilbert equation, Bloch equation.

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APA Style

Hamdache, K., & Hamroun, D. (2019). Asymptotic Behaviours for the Landau-Lifschitz-Bloch Equation. Advances in the Theory of Nonlinear Analysis and its Application3(4), 174-191.