Ferromagnets with eddy current and pinning effects: their thermodynamics and analysis

Existence of weak solutions is proved for a system of nonlinear parabolic equations/inequalities describing evolution of magnetization, temperature, magnetic field, and electric field in electrically-conductive unsaturated ferromagnets. The system is derived from a recently-proposed thermodynamically-consistent continuum theory for the ferro/paramagnetic transition. Besides the standard viscous-like damping, dissipation due to eddy currents and domain-wall pinning is considered.