© 1994

Differential Models of Hysteresis


Part of the Applied Mathematical Sciences book series (AMS, volume 111)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Introduction

    1. Augusto Visintin
      Pages 1-6
  3. Reader’s Guide

    1. Augusto Visintin
      Pages 7-8
  4. Historical Notes

    1. Augusto Visintin
      Pages 9-11
  5. Hysteresis Operators

    1. Augusto Visintin
      Pages 12-31
    2. Augusto Visintin
      Pages 32-58
    3. Augusto Visintin
      Pages 59-96
    4. Augusto Visintin
      Pages 97-129
    5. Augusto Visintin
      Pages 130-150
    6. Augusto Visintin
      Pages 151-185
  6. Partial Differential Equations with Hysteresis

    1. Augusto Visintin
      Pages 186-210
    2. Augusto Visintin
      Pages 211-256
    3. Augusto Visintin
      Pages 257-294
    4. Augusto Visintin
      Pages 295-324
    5. Augusto Visintin
      Pages 325-361
  7. Appendix

    1. Augusto Visintin
      Pages 362-388
    2. Augusto Visintin
      Pages 389-390
  8. Back Matter
    Pages 391-411

About this book


Hysteresis effects occur in science and engineering: plasticity, ferromagnetism, ferroelectricity are well-known examples. Modelling and mathematical analysis of hysteresis phenomena have been addressed by mathematicians only recently, but are now in full development.
This volume provides a self-contained and comprehensive introduction to the analysis of hysteresis models, and illustrates several new results in this field. First the classical models of Prandtl, Ishlinskii, Preisach and Duhem are formulated and studied, using the concept of "hysteresis operator". A new model of discontinuous hysteresis is introduced. Several partial differential equations containing hysteresis operators are studied in the framework of Sobolev spaces.


Hysteresis Mathematical Modelling Memory Nonlinear Partial Differential Equations Plasticity Sobolev space partial differential equation

Authors and affiliations

  1. 1.Dipartimento di MatematicaUniversitá di TrentoPovo (Trento)Italy

Bibliographic information

  • Book Title Differential Models of Hysteresis
  • Authors Augusto Visintin
  • Series Title Applied Mathematical Sciences
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1994
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-3-540-54793-8
  • Softcover ISBN 978-3-642-08132-3
  • eBook ISBN 978-3-662-11557-2
  • Series ISSN 0066-5452
  • Edition Number 1
  • Number of Pages XII, 412
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Applications of Mathematics
    Operator Theory
    Partial Differential Equations
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