| 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:
|
http://hdl.handle.net/10338.dmlcz/104387 |
| . |
| 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 |
| . |
