Abstract
When speaking of hysteresis1, one usually refers to a relation between two scalar time-dependent quantities that cannot be expressed in terms of a single-valued function, but takes the form of loops like the one depicted in Fig. 0.1.
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References
From the Greek word hysterein = to be behind or later, to come late; hysteresis = shortcoming, deficiency, need. See Liddell-Scott-Jones (1843/1951).
See Murakami (1992).
Cf. Mayergoyz (1991).
For a mathematical analysis of this model, see Chapter 6 in Krasnoselskii-Pokrovskii (1989) or Chapter V in Visintin (1994a). In Bliman-Sorine (1993b), this model has been generalized in an attempt to combine the concepts of rate independence and of linear systems theory.
See Duvaut-Lions (1976), Panagiotopoulos (1985), Visintin (1994a) and Krejčí (1996).
See, for instance, the monographs Visintin (1994a) and Krejčí (1996).
For the results of Chapter 6, see also the recent monograph Zheng (1995).
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© 1996 Springer-Verlag New York, Inc.
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Brokate, M., Sprekels, J. (1996). Introduction. In: Hysteresis and Phase Transitions. Applied Mathematical Sciences, vol 121. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4048-8_1
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DOI: https://doi.org/10.1007/978-1-4612-4048-8_1
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