EXISTENCE AND UNIQUENESS FOR A THREE DIMENSIONAL MODEL OF FERROMAGNETISM

A three-dimensional model describing the behavior of a ferromagnetic material is proposed. Since the passage between paramagnetic and ferromagnetic state at the Curie temperature is a second order phase transition, the phenomenon is set in the context of the Ginzburg-Landau theory, identifying the order parameter with the magnetization M. Accordingly, M satisfies a vectorial Ginzburg-Landau equation, interpreted as a balance law of the internal order structure. Thermoelectromagnetic effects are included by coupling Maxwell's equation and the appropriate representation of the heat equation. The resulting differential system is completed with initial and boundary conditions and its well-posedness is proved.