WIAS Preprint No. 702, (2001)

One-dimensional thermo-visco-plastic processes with hysteresis and phase transitions


  • Krejčí, Pavel
    ORCID: 0000-0002-7579-6002
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604
  • Stefanelli, Ulisse

2010 Mathematics Subject Classification

  • 74N30 47J40 34C55 35K60


  • Phase-field systems, phase transitions, hysteresis operators, thermo-visco-plasticity




We consider a strongly coupled system of partial differential equations as a model for the dynamics of a thermo-visco-elasto-plastic solid under phase transitions. It consists of the momentum balance equation for the displacement, the energy balance equation for the absolute temperature, and an order parameter equation describing the dynamics of the phase transition. Both the phase transition and the strain-stress law involve hysteresis dependence represented by hysteresis operators. We show the thermodynamic consistency of the model, and prove its well-posedness.

Appeared in

  • Adv. Math. Sci. Appl., Volume 13, No.2 (2003), 695-712

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