Thermodynamically-consistent mesoscopic model of the ferro/paramagnetic   transition
  A continuum evolutionary model for micromagnetics is presented that, beside the standard magnetic balance laws, includes thermo-magnetic coupling. To allow conceptually efficient computer implementation, inspired by relaxation method of static minimization problems, our model is mesoscopic in the sense that possible fine spatial oscillations of the magnetization are modeled by means of Young measures. Existence of weak solutions is proved by backward Euler time discretization. 
Barbora Bene\v{s}ov\'a, Martin Kru\v{z}\'ik, Tom\'a\v{s}   Roub\'i\v{c}ek
math.AP