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Existence and uniqueness results for a class of rate-independent hysteresis problems. (English) Zbl 1121.34052
Summary: In this paper, we address the problem of existence, approximation, and uniqueness of solutions to an abstract doubly nonlinear equation, modeling a rate-independent process with hysteretic behavior. Models of this kind arise in, e.g. plasticity, solid phase transformations, and several other problems in non smooth mechanics. Existence of solutions is proved via passage to the limit in a time-discretization scheme, whereas uniqueness results are obtained by means of convex analysis techniques.

MSC:
34C55 Hysteresis for ordinary differential equations
47J40 Equations with nonlinear hysteresis operators
49J40 Variational inequalities
74N30 Problems involving hysteresis in solids
34G25 Evolution inclusions
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