A mathematical model for current-induced magnetization dynamics in ferromagnets at elevated temperatures is considered. The model is represented by a classical Landau-Lifshitz-Bloch equation containing adiabatic and non-adiabatic torques. In the case of a ferromagnet confined to a bounded domain of ${\mathbb{R}}^3$, we prove existence of a weak solution by using Faedo-Galerkin approach and a compactness method. This paper extends the work done by Le et al. (2016) in the absence of adiabatic and non-adiabatic terms. Furthermore, uniqueness is proved in the case of dimension one and two. Finally, the limiting behaviour in large time is studied for the non-adiabatic case.

考虑了高温下铁磁体中电流感应磁化动力学的数学模型。该模型由包含绝热和非绝热扭矩的经典Landau-Lifshitz-Bloch方程表示。如果铁磁体被限制在的有界域内${\mathbb{[R}}^3$，我们使用Faedo-Galerkin方法和紧致性方法证明了弱解的存在。本文扩展了Le等人所做的工作。（2016）中没有绝热和非绝热条件。此外，在第一维和第二维的情况下证明了唯一性。最后，研究了非绝热情况下长时间的极限行为。