Overview
- Authors:
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Martin Brokate
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Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Kiel, Germany
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Jürgen Sprekels
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Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
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Table of contents (9 chapters)
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- Martin Brokate, Jürgen Sprekels
Pages 1-9
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- Martin Brokate, Jürgen Sprekels
Pages 10-21
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- Martin Brokate, Jürgen Sprekels
Pages 22-121
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- Martin Brokate, Jürgen Sprekels
Pages 122-149
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- Martin Brokate, Jürgen Sprekels
Pages 150-174
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- Martin Brokate, Jürgen Sprekels
Pages 175-217
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- Martin Brokate, Jürgen Sprekels
Pages 218-270
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- Martin Brokate, Jürgen Sprekels
Pages 271-303
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- Martin Brokate, Jürgen Sprekels
Pages 304-331
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Back Matter
Pages 332-358
About this book
Hysteresis is an exciting and mathematically challenging phenomenon that oc curs in rather different situations: jt, can be a byproduct offundamental physical mechanisms (such as phase transitions) or the consequence of a degradation or imperfection (like the play in a mechanical system), or it is built deliberately into a system in order to monitor its behaviour, as in the case of the heat control via thermostats. The delicate interplay between memory effects and the occurrence of hys teresis loops has the effect that hysteresis is a genuinely nonlinear phenomenon which is usually non-smooth and thus not easy to treat mathematically. Hence it was only in the early seventies that the group of Russian scientists around M. A. Krasnoselskii initiated a systematic mathematical investigation of the phenomenon of hysteresis which culminated in the fundamental monograph Krasnoselskii-Pokrovskii (1983). In the meantime, many mathematicians have contributed to the mathematical theory, and the important monographs of 1. Mayergoyz (1991) and A. Visintin (1994a) have appeared. We came into contact with the notion of hysteresis around the year 1980.
Authors and Affiliations
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Mathematisches Seminar, Christian-Albrechts-Universität zu Kiel, Kiel, Germany
Martin Brokate
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Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
Jürgen Sprekels