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Discontinuous Hysteresis and P.D.E.s

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Book cover Variational Problems in Materials Science

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 68))

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Abstract

Hysteresis can be represented via hysteresis operators. Some basic models of discontinuous hysteresis are here reviewed: the relay operator, the Preisach model, and their vector extensions. In view of the analysis of related problems at the P.D.E.s, a weak formulation is also provided. The conservation law

$$ \frac{\partial } {{\partial t}}[u + \mathcal{F}(u)] + \frac{{\partial u}} {{\partial x}} = f in R \times ]0,T[ $$

is then briefly discussed, F being a discontinuous hysteresis operator.

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica dell’Università degli Studi di Trento, via Sommarive 14, I-38050, Povo di Trento, Italia

    Augusto Visintin

Authors
  1. Augusto Visintin
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Editor information

Editors and Affiliations

  1. Scuola Internazionale Superiore di Studi Avanzati (SISSA), Via Beirut 4, 34014, Trieste, Italy

    Gianni dal Maso  & Antonio DeSimone  & 

  2. Dipartimento di Matematica “Francesco Brioschi”, Politecnico di Milano, Piazza Leonardo da Vinci 32, 20133, Milano, Italy

    Franco Tomarelli

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© 2006 Birkhäuser Verlag Basel/Switzerland

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Visintin, A. (2006). Discontinuous Hysteresis and P.D.E.s. In: dal Maso, G., DeSimone, A., Tomarelli, F. (eds) Variational Problems in Materials Science. Progress in Nonlinear Differential Equations and Their Applications, vol 68. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7565-5_11

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