Mathematical Analysis for a Class of Partial Differential Equations with Dynamic Preisach Model

This work deals with the mathematical analysis and numerical solution of a parabolic problem with dynamic hysteresis motivated by electromagnetic field equations. In this case, the values of the magnetic induction depend not only on the current values of the magnetic field, but also on the previous ones and on the velocity at which they have been attained. The hysteresis is modelled by the dynamic Preisach operator. Based upon the definition of dynamic relay, which is introduced and formalized as the solution of a multi-valued ordinary differential equation, the definition of the dynamic Preisach operator is recalled and some of their main properties established. Under suitable assumptions, the well-posedness of a weak formulation of the initial problem is shown and a numerical solution computed.