On a low-dimensional model for ferromagnetism
The authors suggest and study a new one-dimensional differential model of rate-independent hysteresis in ferromagnetic materials with two state variables. The model is systematically derived from thermodynamics and energy balance consideration (with some additional assumptions), where hysteresis losses are assumed to have the form postulated by Jiles and Atherton, which essentially means that the losses are proportional to the change of magnetization. Qualitative properties of the model are analyzed, including a proof of the existence and uniqueness of solutions. The main theorem states convergence to a periodic solution from the zero initial state for sinusoidal inputs provided some model parameter is small enough, which is for example the case for small hysteresis losses. This result is then extended to a larger class of inputs.
scientific article; zbMATH DE number 2175334