Control of a Multi-Component Phase Transition Model with Hysteresis

Chen Bin, Emil Minchev, Sergey A. Timoshin*, Jin Xiaohan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


The present paper addresses a phase-field system modelling the dynamics of solid-liquid phase transitions of several substances coexisting in the same container. We allow for a hysteretic effect in the vector order parameter—absolute temperature relationship. Our system is subjected to an external control action constrained to a nonconvex-valued mapping. The existence of solutions for this control problem is established and some of their relaxation type properties are explored under a minimal set of requirements on the curves describing the hysteresis region of the problem.

Original languageEnglish
JournalApplied Mathematics and Optimization
Issue number1
Publication statusPublished - Feb 2022
Externally publishedYes


  • Control problems
  • Evolution systems
  • Hysteresis
  • Phase transitions
  • Relaxation
  • Well-posedness


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