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Differential Models of Hysteresis

  • Book
  • © 1994

Overview

Authors:
  1. Augusto Visintin

    1. Dipartimento di Matematica, Universitá di Trento, Povo (Trento), Italy

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

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    1. Introduction

      • Augusto Visintin
      Pages 1-6

  3. Reader’s Guide

    1. Reader’s Guide

      • Augusto Visintin
      Pages 7-8

  4. Historical Notes

    1. Historical Notes

      • Augusto Visintin
      Pages 9-11

  5. Hysteresis Operators

    1. Genesis of Hysteresis

      • Augusto Visintin
      Pages 12-31

    2. Rheological and Circuital Models

      • Augusto Visintin
      Pages 32-58

    3. Plays, Stops and Prandtl-Ishlinskiĭ Models

      • Augusto Visintin
      Pages 59-96

    4. The Preisach Model

      • Augusto Visintin
      Pages 97-129

    5. The Duhem Model

      • Augusto Visintin
      Pages 130-150

    6. Discontinuous Hysteresis

      • Augusto Visintin
      Pages 151-185

  6. Partial Differential Equations with Hysteresis

    1. P.D.E. Models of Elasto-Plasticity

      • Augusto Visintin
      Pages 186-210

    2. Hysteresis and Semigroups

      • Augusto Visintin
      Pages 211-256

    3. Quasilinear P.D.E.s with Memory

      • Augusto Visintin
      Pages 257-294

    4. Semilinear P.D.E.s with Memory

      • Augusto Visintin
      Pages 295-324

    5. P.D.E.s with Discontinuous Hysteresis

      • Augusto Visintin
      Pages 325-361

  7. Appendix

    1. Some Tools

      • Augusto Visintin
      Pages 362-388

    2. Conclusion

      • Augusto Visintin
      Pages 389-390

  8. Back Matter

    Pages 391-411
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Keywords

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.

Authors and Affiliations

  • Dipartimento di Matematica, Universitá di Trento, Povo (Trento), Italy

    Augusto Visintin

Bibliographic Information

  • Book Title: Differential Models of Hysteresis

  • Authors: Augusto Visintin

  • Series Title: Applied Mathematical Sciences

  • DOI: https://doi.org/10.1007/978-3-662-11557-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Hardcover ISBN: 978-3-540-54793-8Published: 28 December 1994

  • Softcover ISBN: 978-3-642-08132-3Published: 01 December 2010

  • eBook ISBN: 978-3-662-11557-2Published: 29 June 2013

  • Series ISSN: 0066-5452

  • Series E-ISSN: 2196-968X

  • Edition Number: 1

  • Number of Pages: XII, 412

  • Topics: Applications of Mathematics, Operator Theory, Partial Differential Equations

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