Hysteresis and Phase Transitions

  • Martin Brokate
  • Jürgen Sprekels

Part of the Applied Mathematical Sciences book series (AMS, volume 121)

Table of contents

  1. Front Matter
    Pages i-x
  2. Martin Brokate, Jürgen Sprekels
    Pages 1-9
  3. Martin Brokate, Jürgen Sprekels
    Pages 10-21
  4. Martin Brokate, Jürgen Sprekels
    Pages 22-121
  5. Martin Brokate, Jürgen Sprekels
    Pages 122-149
  6. Martin Brokate, Jürgen Sprekels
    Pages 150-174
  7. Martin Brokate, Jürgen Sprekels
    Pages 175-217
  8. Martin Brokate, Jürgen Sprekels
    Pages 218-270
  9. Martin Brokate, Jürgen Sprekels
    Pages 271-303
  10. Martin Brokate, Jürgen Sprekels
    Pages 304-331
  11. Back Matter
    Pages 332-358

About this book

Introduction

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.

Keywords

Approximation Convexity Phase Transition Phase Transitions differential equation function space linear optimization wave equation

Authors and affiliations

  • Martin Brokate
    • 1
  • Jürgen Sprekels
    • 2
  1. 1.Mathematisches SeminarChristian-Albrechts-Universität zu KielKielGermany
  2. 2.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-4048-8
  • Copyright Information Springer-Verlag New York 1996
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-8478-9
  • Online ISBN 978-1-4612-4048-8
  • Series Print ISSN 0066-5452
  • About this book