Ebook: Differential Models of Hysteresis

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.

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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.

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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.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-6
Reader’s Guide....Pages 7-8
Historical Notes....Pages 9-11
Genesis of Hysteresis....Pages 12-31
Rheological and Circuital Models....Pages 32-58
Plays, Stops and Prandtl-Ishlinski? Models....Pages 59-96
The Preisach Model....Pages 97-129
The Duhem Model....Pages 130-150
Discontinuous Hysteresis....Pages 151-185
P.D.E. Models of Elasto-Plasticity....Pages 186-210
Hysteresis and Semigroups....Pages 211-256
Quasilinear P.D.E.s with Memory....Pages 257-294
Semilinear P.D.E.s with Memory....Pages 295-324
P.D.E.s with Discontinuous Hysteresis....Pages 325-361
Some Tools....Pages 362-388
Conclusion....Pages 389-390
Back Matter....Pages 391-411

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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.
Content:
Front Matter....Pages i-xi
Introduction....Pages 1-6
Reader’s Guide....Pages 7-8
Historical Notes....Pages 9-11
Genesis of Hysteresis....Pages 12-31
Rheological and Circuital Models....Pages 32-58
Plays, Stops and Prandtl-Ishlinski? Models....Pages 59-96
The Preisach Model....Pages 97-129
The Duhem Model....Pages 130-150
Discontinuous Hysteresis....Pages 151-185
P.D.E. Models of Elasto-Plasticity....Pages 186-210
Hysteresis and Semigroups....Pages 211-256
Quasilinear P.D.E.s with Memory....Pages 257-294
Semilinear P.D.E.s with Memory....Pages 295-324
P.D.E.s with Discontinuous Hysteresis....Pages 325-361
Some Tools....Pages 362-388
Conclusion....Pages 389-390
Back Matter....Pages 391-411
....