WIAS Preprint No. 2737, (2020)

Optimal control for shape memory alloys of the one-dimensional Frémond model


  • Colli, Pierluigi
    ORCID: 0000-0002-7921-5041
  • Farshbaf Shaker, Mohammad Hassan
    ORCID: 0000-0003-0543-5938
  • Shirakawa, Ken
  • Yamazaki, Noriaki

2010 Mathematics Subject Classification

  • 49J20 35K55 35R35


  • Optimal control problem, one-dimensional Frémond model, shape memory alloys, Mosco convergence, subdifferentials




In this paper, we consider optimal control problems for the one-dimensional Frémond model for shape memory alloys. This model is constructed in terms of basic functionals like free energy and pseudo-potential of dissipation. The state problem is expressed by a system of partial differential equations involving the balance equations for energy and momentum. We prove the existence of an optimal control that minimizes the cost functional for a nonlinear and nonsmooth state problem. Moreover, we show the necessary condition of the optimal pair by using optimal control problems for approximating systems.

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