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Title: Hysteresis memory preserving operators (English)
Author: Krejčí, Pavel
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 36
Issue: 4
Year: 1991
Pages: 305-326
Summary lang: English
Category: math
Summary: The recent development of mathematical methods of investigation of problems with hysteresis has shown that the structure of the hysteresis memory plays a substantial role. In this paper we characterize the hysteresis operators which exhibit a memory effect of the Preisach type (memory preserving operators). We investigate their properties (continuity, invertibility) and we establish some relations between special classes of such operators (Preisach, Ishlinskii and Nemytskii operators). For a general memory preserving operator we derive an energy inequality. (English)
Keyword: hysteresis memory
Keyword: Preisach operators
Keyword: memory preserving operators
Keyword: energy inequality
Keyword: hysteresis operators
Keyword: Prandtl model
Keyword: Ishlinskij model
Keyword: moving model
MSC: 35R45
MSC: 47H30
MSC: 58C07
MSC: 58D25
MSC: 58D30
idZBL: Zbl 0756.47053
idMR: MR1113953
DOI: 10.21136/AM.1991.104468
Date available: 2008-05-20T18:42:04Z
Last updated: 2020-07-28
Stable URL:
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Reference: [5] M. A. Krasnoselskii A. V. Pokrovskii: Systems with hysteresis.(Russian). Moscow, Nauka, 1983. MR 0742931
Reference: [6] P. Krejčí: Hysteresis and periodic solutions to semilinear and quasilinear wave equations.Math. Z. 193 (1986), 247-264. MR 0856153, 10.1007/BF01174335
Reference: [7] P. Krejčí: On Maxwell equations with the Preisach hysteresis operator: the one-dimensional time-periodic case.Apl. Mat. 34 (1989), 364-374. MR 1014077
Reference: [8] P. Krejčí: Hysteresis operators - a new approach to evolution differential inequalities.Comment. Math. Univ. Carolinae, 30, 3 (1989), 525-536. MR 1031870
Reference: [9] D. Mayergoyz: Mathematical models for hysteresis.Phys. Rev. Letters 56 (1986), 1518-1529. 10.1103/PhysRevLett.56.1518


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