Properties of the Preisach model for hysteresis. (English) Zbl 0682.47034

Brokate, Martin; Visintin, Augusto

J. Reine Angew. Math. 402, 1-40 (1989).

As shown by Krasnosel’skij and Pokrovskii, the classical Presach model allows to construct a hysteresis operator W between spaces of real functions of time. This construction, via the definition of a measure \(\mu\) in the so-called Preisach plane, is recalled. Characterizations in terms of \(\mu\) are given for several mapping and continuity properties of W in various function spaces, for the invertibility of W and for the corresponding mapping and continuity properties of the inverse.

Reviewer: M.Brokate

MSC:

47H99

Nonlinear operators and their properties

Keywords:

Presach model; hysteresis operator; Preisach plane; invertibility; continuity properties of the inverse