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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
ATNAA
2019-10-01
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| Series: | Advances in the Theory of Nonlinear Analysis and its Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/824934 |
| Summary: | 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 δ 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, δ and a being independent of the
temperature, we show that the limit of (LLB) equation is Landau-Lifshitz-Gilbert equation. |
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| ISSN: | 2587-2648 2587-2648 |