Hysteresis and Phase Transitions, Martin Brokate; J?rgen Sprekels

Автор: Augusto Visintin; M. Brokate; N. Kenmochi; I. M?ll
Название: Phase Transitions and Hysteresis
ISBN: 3540583866 ISBN-13(EAN): 9783540583868
Издательство: Springer
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Описание: 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. In a general framework, hysteresis can be described by means of hysteresis operators in Banach spaces of time dependent functions;

Автор: Augusto Visintin
Название: Differential Models of Hysteresis
ISBN: 3642081320 ISBN-13(EAN): 9783642081323
Издательство: Springer
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Описание: 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.

Автор: Augusto Visintin
Название: Models of Phase Transitions
ISBN: 1461286417 ISBN-13(EAN): 9781461286417
Издательство: Springer
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Описание: ... "What do you call work?" "Why ain't that work?" Tom resumed his whitewashing, and answered carelessly: "Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom Sawvc/: " "Oil CO/lll , IIOW, Will do not mean to let 011 that you like it?" The brush continued to move. "Likc it? Well, I do not see wlzy I oughtn't to like it. Does a hoy get a chance to whitewash a fence every day?" That put the thing ill a Ilew light. Ben stopped nibhling the apple .... (From Mark Twain's Adventures of Tom Sawyer, Chapter II.) Mathematics can put quantitative phenomena in a new light; in turn applications may provide a vivid support for mathematical concepts. This volume illustrates some aspects of the mathematical treatment of phase transitions, namely, the classical Stefan problem and its generalizations. The in- tended reader is a researcher in application-oriented mathematics. An effort has been made to make a part of the book accessible to beginners, as well as physicists and engineers with a mathematical background. Some room has also been devoted to illustrate analytical tools. This volume deals with research I initiated when I was affiliated with the Istituto di Analisi Numerica del C.N.R. in Pavia, and then continued at the Dipartimento di Matematica dell'Universita di Trento. It was typeset by the author in plain TEX.