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EXISTENCE AND UNIQUENESS RESULTS FOR A CLASS OF RATE-INDEPENDENT HYSTERESIS PROBLEMS

ALEXANDER MIELKE

Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany

Institut für Mathematik, Humboldt-Universität zu Berlin, Rudower Chaussee 25, 12489 Berlin (Adlershof), Germany

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and

RICCARDA ROSSI

Dipartimento di Matematica, Università di Brescia, Via Valotti 9, Brescia, I-20133, Italy

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https://doi.org/10.1142/S021820250700184XCited by:48 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 34C55, 47J20, 49J40, 74N30

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