  Hysteresis is a phenomenon that is observed in a great variety of physical
systems, which leads to a nonlinear and multivalued behavior, making their
modeling and control difficult. Even though the analysis and mathematical
properties of classical or rate-independent hysteresis models are known, this
is not the case for dynamic models where current approaches lack a proper
functional analytic framework which is essential to formulate optimization
problems and develop stable numerics, both being crucial in practice. This
paper deals with the description and mathematical analysis of the dynamic
Preisach hysteresis model. Toward that end, we complete a widely accepted
definition of the dynamic model commonly used to describe the constitutive
relation between the magnetic field H and the magnetic induction B, in which,
the values of B not only depends on the present values of H but also on the
past history and its velocity. We first analyze mathematically some important
properties of the model and compare them with known results for the static
Preisach model. Then, we consider a parabolic problem with dynamic hysteresis
motivated by electromagnetic field equations. Under suitable assumptions, we
show the well posedness of a weak formulation of the problem and solve it
numerically.
  Finally, we report a numerical test in order to assess the order of
convergence and to illustrate the behavior of the numerical solution for
different configurations of the dynamic Preisach model
