On the Landau-Lifshitz-Bloch equation with spin torque effects

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 R³, 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.