Asymptotic Behaviours for the Landau-Lifschitz-Bloch Equation

Authors : Kamel HAMDACHE, Djamila HAMROUN

Pages : 174-191

Doi:10.31197/atnaa.512065

View : 10 | Download : 5

Publication Date : 2019-12-30

Article Type : Research Paper

Abstract :The Landau-Lifshitz-Bloch insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(LLB); equation  is  Landau-Lifshitz-Gilbert equation.
Keywords : Landau Lifshitz Bloch equation, Landau Lifshitz Gilbert equation, Bloch equation