Differential Models of Hysteresis

by Augusto Visintin

Overview

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.

Product Details

ISBN-13:	9783642081323
Publisher:	Springer Berlin Heidelberg
Publication date:	12/09/2010
Series:	Applied Mathematical Sciences , #111
Edition description:	Softcover reprint of hardcover 1st ed. 1994
Pages:	412
Product dimensions:	6.10(w) x 9.25(h) x 0.24(d)

Table of Contents

Reader’s Guide.- Historical Notes.- I. Genesis of Hysteresis.- II. Rheological and Circuital Models.- III. Plays, Stops and Prandtl-Ishlinski? Models.- IV. The Preisach Model.- V. The Duhem Model.- VI. Discontinuous Hysteresis.- VII. P.D.E. Models of Elasto-Plasticity.- VIII. Hysteresis and Semigroups.- IX. Quasilinear P.D.E.s with Memory.- X. Semilinear P.D.E.s with Memory.- XI. P.D.E.s with Discontinuous Hysteresis.- XII. Some Tools.- Conclusion.