WIAS Preprint No. 748, (2002)

Outwards pointing hysteresis operators and asymptotic behaviour of evolution equations


  • Klein, Olaf
    ORCID: 0000-0002-4142-3603
  • Krejčí, Pavel
    ORCID: 0000-0002-7579-6002

2010 Mathematics Subject Classification

  • 34C55 35B40 74N30 47J40 35K60 74K05


  • hysteresis operators, Prandtl-Ishlinskii operator, asymptotic behaviour, visco-elasto-plasticity




The paper deals with the long-time behaviour of evolution systems described by ODEs and PDEs with hysteresis operators. The analysis is based on two concepts. The first one is the outward pointing property of the involved hysteresis operators which implies uniform a priori bounds for solutions, the second one is related to the hysteresis modelling itself and consists in introducing a class of thermodynamically consistent generalized Prandtl-Ishlinskii operators as a model for a nonlinear elastoplastic material law. A stability result for solutions in one-dimensional visco-elasto-plasticity is derived as an illustration of the theory.

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