- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 3 Issue: 4
- Asymptotic Behaviours for the Landau-Lifschitz-Bloch Equation
Asymptotic Behaviours for the Landau-Lifschitz-Bloch Equation
Authors : Kamel HAMDACHE, Djamila HAMROUN
Pages : 174-191
Doi:10.31197/atnaa.512065
View : 5 | Download : 3
Publication Date : 2019-12-30
Article Type : Research
Abstract :The Landau-Lifshitz-Bloch (LLB) equation is an interpolation between Bloch equation valid for high temperatures and Landau-Lifshitz equation valid for low temperatures. Conversely in this paper, we discuss the behaviours of the solutions of (LLB) equation both as the temperature goes to infinity or 0. Surprisingly in the first case, the behaviour depends also on the scaling of the damping parameter $\delta$ and the volume exchange parameter $a$. Three cases are considered and accordingly we get either a linear stationary equation, Bloch equation or Stokes equation. As for the small temperature behaviour, $\delta$ and $a$ being independent of the temperature, we show that the limit of (LLB) equation is Landau-Lifshitz-Gilbert equation.Keywords : Landau-Lifshitz-Bloch equation, Landau-Lifshitz-Gilbert equation, Bloch equation