We look for a parametric description of a class of hysteresis operators possessing a natural set of properties, including short memory. The results of this type are known as realization or characterization theorems; up to date, mainly onedimensional operators have been characterized. We demonstrate

: We consider continuous-time hysteresis operators, dened to be causal and rate independent operators mapping input signals u : R+ ! R to output signals v : R+ ! R. We show how a hysteresis operator dened on the space of continuous piecewise monotone functions, can be naturally extended

-type hysteresis operators which, in terms of mathematics, can be easily described and which reflect the qualitative properties of the inverse transfer characteristic of the transducer. Starting with a linear characteristic the weigths of an inverse hysteretic observer are identified during operation by a stable

Parabolic initial boundary-value problems coupled (via the boundary condition) with ordinary differential equations whose right-hand side contains the Preisach hysteresis operator are considered. In particular, these problems model thermocon-trol processes in chemical reactors, climate

is replaced by a scalar Prandtl-Ishlinskii hysteresis spatially dependent operator. We prove existence, uniqueness and regularity of solution to the corresponding initial-boundary value problem. The problem is then homogenized by considering a sequence of equations of the above type with spatially periodic

We consider a model for one-dimensional transversal oscillations of an elastic-ideally plastic beam. It is based on the von Mises model of plasticity and leads after a dimensional reduction to a fourth-order partial differential equation with a hysteresis operator of Prandtl-Ishlinskii type whose

-type hysteresis operators which, in terms of mathematics, can be easily described and which reflect the qualitative properties of the inverse transfer characteristic of the transducer. Starting with a linear characteristic the weigths of an inverse hysteretic observer are identified during operation by a stable

transition processes. To overcome this shortcoming of existing phase-field theories, the authors recently proposed a new approach to phase-field models which is based on the mathematical theory of hysteresis operators developed in the past fifteen years. Well-posedness and thermodynamic consistency were

. In this paper, we consider the problem of constructing right inverses for the Preisach model for hysteresis. Under mild conditions on the density function, we show the existence and weak-star continuity of the right-inverse, when the Preisach operator is considered to act on Hölder continuous functions. Next

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