| 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:
|
http://hdl.handle.net/10338.dmlcz/104468 |
| . |
| Reference:
|
[1] M. Brokate: On a characterization of the Preisach model for hysteresis.Bericht Nr. 35, Universität Kaiserslautern, 1989. MR 1066436 |
| Reference:
|
[2] M. Brokate A. Visintin: Properties of the Preisach model for hysteresis.J. reine angen. Math. 402 (1989) 1-40. MR 1022792 |
| Reference:
|
[3] E. Della Torre J. Oti G. Kádár: Preisach modelling and reversible magnetization.Preprint. |
| Reference:
|
[4] M. Hilpert: On uniqueness for evolution problems with hysteresis.Report No. 119, Universität Augsburg, 1989. Zbl 0701.35009, MR 1038080 |
| 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 |
| . |
