Continuity of hysteresis operators in Sobolev spaces

Pavel Krejčí; Vladimír Lovicar

Aplikace matematiky (1990)

  • Volume: 35, Issue: 1, page 60-66
  • ISSN: 0862-7940

Abstract

top
We prove that the classical Prandtl, Ishlinskii and Preisach hysteresis operators are continuous in Sobolev spaces W 1 , p ( 0 , T ) for 1 p < + , (localy) Lipschitz continuous in W 1 , 1 ( 0 , T ) and discontinuous in W 1 , ( 0 , T ) for arbitrary T > 0 . Examples show that this result is optimal.

How to cite

top

Krejčí, Pavel, and Lovicar, Vladimír. "Continuity of hysteresis operators in Sobolev spaces." Aplikace matematiky 35.1 (1990): 60-66. <http://eudml.org/doc/15610>.

@article{Krejčí1990,
abstract = {We prove that the classical Prandtl, Ishlinskii and Preisach hysteresis operators are continuous in Sobolev spaces $W^\{1,p\}(0,T)$ for $1\le 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.},
author = {Krejčí, Pavel, Lovicar, Vladimír},
journal = {Aplikace matematiky},
keywords = {hysteresis operators; Preisach operator; Ishlinskii operator; hysteresis oprators},
language = {eng},
number = {1},
pages = {60-66},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Continuity of hysteresis operators in Sobolev spaces},
url = {http://eudml.org/doc/15610},
volume = {35},
year = {1990},
}

TY - JOUR
AU - Krejčí, Pavel
AU - Lovicar, Vladimír
TI - Continuity of hysteresis operators in Sobolev spaces
JO - Aplikace matematiky
PY - 1990
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 35
IS - 1
SP - 60
EP - 66
AB - We prove that the classical Prandtl, Ishlinskii and Preisach hysteresis operators are continuous in Sobolev spaces $W^{1,p}(0,T)$ for $1\le 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.
LA - eng
KW - hysteresis operators; Preisach operator; Ishlinskii operator; hysteresis oprators
UR - http://eudml.org/doc/15610
ER -

References

top
  1. M. A. Krasnoselskii A. V. Pokrovskii, Systems with hysteresis, (Russian) Moscow, Nauka, 1983. (1983) MR0742931
  2. A. V. Pokrovskii, On the theory of hysteresis nonlinearities, (Russian) Dokl. Akad. Nauk SSSR 210 (1973), no. 6, 1284-1287. (1973) Zbl0293.45014MR0333869
  3. P. Krejčí, On Maxwell equations with the Preisach hysteresis operator: the one-dimensional time-periodic case, Apl. Mat. 34 (1989), 364-374. (1989) Zbl0701.35098MR1014077
  4. A. Visintin, On the Preisach model for hysteresis, Nonlinear Anal. T. M. A. 8 (1984), 977-996. (1984) Zbl0563.35007MR0760191

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.