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Hysteresis memory preserving operators. (English) Zbl 0756.47053

The author studies classes of hysteresis operators which exhibit “Preisach type” memory effects. In particular, he specifies the relationship with various hysteresis models, such as the Prandtl model, the Ishlinskij model, or moving model [see the preceding review].

MSC:

47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.)
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References:

[1] M. Brokate: On a characterization of the Preisach model for hysteresis. Bericht Nr. 35, Universität Kaiserslautern, 1989. · Zbl 0719.47053
[2] M. Brokate A. Visintin: Properties of the Preisach model for hysteresis. J. reine angen. Math. 402 (1989) 1-40. · Zbl 0682.47034
[3] E. Della Torre J. Oti G. Kádár: Preisach modelling and reversible magnetization. Preprint.
[4] M. Hilpert: On uniqueness for evolution problems with hysteresis. Report No. 119, Universität Augsburg, 1989. · Zbl 0701.35009
[5] M. A. Krasnoselskii A. V. Pokrovskii: Systems with hysteresis. (Russian). Moscow, Nauka, 1983.
[6] P. Krejčí: Hysteresis and periodic solutions to semilinear and quasilinear wave equations. Math. Z. 193 (1986), 247-264. · Zbl 0658.35065
[7] P. Krejčí: On Maxwell equations with the Preisach hysteresis operator: the one-dimensional time-periodic case. Apl. Mat. 34 (1989), 364-374. · Zbl 0701.35098
[8] P. Krejčí: Hysteresis operators - a new approach to evolution differential inequalities. Comment. Math. Univ. Carolinae, 30, 3 (1989), 525-536. · Zbl 0699.35270
[9] D. Mayergoyz: Mathematical models for hysteresis. Phys. Rev. Letters 56 (1986), 1518-1529.
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