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Phase Transitions and Hysteresis

Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini Terme, Italy, July 13 - 21, 1993

  • Book
  • © 1994

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Authors:
  1. M. Brokate
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  2. Yong Zhong Huo
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  3. Noboyuki Kenmochi
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  4. Ingo Müller
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  5. José F. Rodriguez
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  6. Claudio Verdi
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Editors:
  1. Augusto Visintin
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1584)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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Table of contents (5 chapters)

  1. Front Matter

    Pages I-VII
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  2. Hysteresis operators

    • Martin Brokate
    Pages 1-38

  3. Systems of nonlinear PDEs arising from dynamical phase transitions

    • Nobuyuki Kenmochi
    Pages 39-86

  4. Quasiplasticity and pseudoelasticity in shape memory alloys

    • Y. Huo, I. Müller, S. Seelecke
    Pages 87-146

  5. Variational methods in the stefan problem

    • José-Francisco Rodrigues
    Pages 147-212

  6. Numerical aspects of parabolic free boundary and hysteresis problems

    • Claudio Verti
    Pages 213-284

  7. Back Matter

    Pages 286-295
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Keywords

About this book

1) Phase Transitions, represented by generalizations of the classical Stefan problem. This is studied by Kenmochi and Rodrigues by means of variational techniques.
2) Hysteresis Phenomena. Some alloys exhibit shape memory effects, corresponding to a stress-strain relation which strongly depends on temperature; mathematical physical aspects are treated in Müller's paper. In a general framework, hysteresis can be described by means of hysteresis operators in Banach spaces of time dependent functions; their properties are studied by Brokate.
3) Numerical analysis. Several models of the phenomena above can be formulated in terms of nonlinear parabolic equations. Here Verdi deals with the most updated approximation techniques.

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