A control problem in phase transition modeling

  • Pavel Krejčí
  • Alexander A. TolstonogovEmail author
  • Sergey A. Timoshin


We consider a nonlinear partial differential control system describing phase transitions taking account of hysteresis effects. The control constraint is given by a multivalued mapping with nonconvex closed bounded values in a finite dimensional space depending on the phase variables. Existence of solutions and topological properties of the set of admissible “trajectory-control” pairs are discussed in detail.


Nonlinear evolution control systems Subdifferential Nonconvex constraints Extreme points Hysteresis 

Mathematics Subject Classification

Primary 49J20 Secondary 49J30 


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  • Pavel Krejčí
    • 1
  • Alexander A. Tolstonogov
    • 2
    Email author
  • Sergey A. Timoshin
    • 2
  1. 1.Institute of MathematicsCzech Academy of SciencesPrague 1Czech Republic
  2. 2.Institute for System Dynamics and Control TheorySiberian Branch, Russian Academy of SciencesIrkutskRussia

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