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AuthorVisintin, Augusto. author
TitleDifferential Models of Hysteresis [electronic resource] / by Augusto Visintin
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1994
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Descript XII, 412 p. online resource


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


Readerโ{128}{153}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

Mathematics Operator theory Partial differential equations Applied mathematics Engineering mathematics Mathematics Applications of Mathematics Operator Theory Partial Differential Equations


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