On a sharp interface model for dynamics in ferro-paramagnetism

Heating up a ferromagnetic body through its Curie temperature changes the material's permanent magnetism to induced magnetism and the material becomes paramagnetic. At the Curie temperature the material might consist of two seperate phases, a ferromagnetic and a paramagnetic phase. To understand the evolution of the phase boundary at this temperature, a quasistatic sharp interface model is introduced. The movement of the phase boundary is described by the mean curvature flow equation including a nonlocal outer force, which is induced by the magnetization structure in the ferromagnetic phase. Luckhaus and Sturzenhecker developed an implicit time discretization for curvature driven flows with a local outer force. This method has been used to construct short-time solutions to several problems. For this model, a phase field approximation of the micromagnetic energy provides functionals to which the discretization can be applied and so compactness of the sets can be derived.