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＜電子ブック＞
Differential Models of Hysteresis / by Augusto Visintin
(Applied Mathematical Sciences. ISSN:2196968X ; 111)

版	1st ed. 1994.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1994
本文言語	英語
大きさ	XII, 412 p : online resource
著者標目	*Visintin, Augusto author SpringerLink (Online service)
件　名	LCSH:Mathematics LCSH:Operator theory LCSH:Differential equations FREE:Applications of Mathematics FREE:Operator Theory FREE:Differential Equations
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-3-662-11557-2

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