Asymptotic Behaviours for the Landau-Lifschitz-Bloch Equation
Asymptotic Behaviours for the Landau-Lifschitz-Bloch Equation
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, thebehaviour 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.
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- Reference 2: M. Feischl and T. Tran, Existence of regular solutions of the Landau-Lifshitz-Gilbert equation in 3D with natural boundary conditions, in SIAM J. Math. Anal. 49 (6) (2017) 4470--4490.
- Reference 3: D.A. Garanin, Fokker-Planck and Landau-Lifshitz-Bloch equations for classical ferromagnets, in Phy. Rev. B 55 (1997) 3050--3057.
- Başlangıç: 2017
- Yayıncı: Erdal KARAPINAR
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