Abstract
Continuous and discontinuous hysteresis operators are first reviewed in general. The Duhem model, the generalized play, the (delayed) relay and the Preisach model are outlined, as well as vector extensions of the two latter models.   Two examples of initial- and boundary-value problems for P.D.E.s with hysteresis are then illustrated. Well-posedness is proved for quasilinear parabolic problems with either continuous or discontinuous hysteresis. Existence of a weak solution is shown for second-order quasilinear hyperbolic problems with discontinuous hysteresis.
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