| Issue |
Math. Model. Nat. Phenom.
Volume 15, 2020
Systems with Hysteresis and Switching
|
|
|---|---|---|
| Article Number | 51 | |
| Number of page(s) | 34 | |
| DOI | https://doi.org/10.1051/mmnp/2020013 | |
| Published online | 11 November 2020 | |
Newton and Bouligand derivatives of the scalar play and stop operator
1
Department of Mathematics, Technical University of Munich,
Boltzmannstr. 3,
85747
Garching, Germany.
2
Weierstrass Institute for Applied Analysis and Stochastics,
Mohrenstr. 39,
10117
Berlin, Germany.
* Corresponding author: brokate@ma.tum.de
Received:
16
April
2019
Accepted:
6
April
2020
We prove that the play and the stop operator possess Newton and Bouligand derivatives, and exhibit formulas for those derivatives. The remainder estimate is given in a strengthened form, and a corresponding chain rule is developed. The construction of the Newton derivative ensures that the mappings involved are measurable.
Mathematics Subject Classification: 47H30 / 47J40 / 49J52 / 49M15 / 58C20
Key words: Rate independence / hysteresis operator / Newton derivative / Bouligand derivative / play, stop / sensitivity / maximum functional / variational inequality / measurable selector / semismooth / chain rule
© The authors. Published by EDP Sciences, 2020
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