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Title: Continuity of hysteresis operators in Sobolev spaces (English)
Author: Krejčí, Pavel
Author: Lovicar, Vladimír
Language: English
Journal: Aplikace matematiky
ISSN: 0373-6725
Volume: 35
Issue: 1
Year: 1990
Pages: 60-66
Summary lang: English
Category: math
Summary: We prove that the classical Prandtl, Ishlinskii and Preisach hysteresis operators are continuous in Sobolev spaces $W^{1,p}(0,T)$ for $1\leq p < +\infty$, (localy) Lipschitz continuous in $W^{1,1}(0,T)$ and discontinuous in $W^{1,\infty}(0,T)$ for arbitrary $T>0$. Examples show that this result is optimal. (English)
Keyword: hysteresis operators
Keyword: Preisach operator
Keyword: Ishlinskii operator
MSC: 46E35
MSC: 47H30
MSC: 58C07
MSC: 73E50
MSC: 73E99
MSC: 74H15
MSC: 74H99
idZBL: Zbl 0705.47054
idMR: MR1039411
DOI: 10.21136/AM.1990.104387
Date available: 2008-05-20T18:38:24Z
Last updated: 2020-07-28
Stable URL:
Reference: [1] M. A. Krasnoselskii A. V. Pokrovskii: Systems with hysteresis.(Russian) Moscow, Nauka, 1983. MR 0742931
Reference: [2] A. V. Pokrovskii: On the theory of hysteresis nonlinearities.(Russian) Dokl. Akad. Nauk SSSR 210 (1973), no. 6, 1284-1287. MR 0333869
Reference: [3] 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: [4] A. Visintin: On the Preisach model for hysteresis.Nonlinear Anal. T. M. A. 8 (1984), 977-996. Zbl 0563.35007, MR 0760191


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