WIAS Preprint No. 259, (1996)

Optimal Control of Martensitic Phase Transitions in a Deformation-Driven Experiment on Shape Memory Alloys


Authors

  • Bubner, Nikolaus
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

2010 Mathematics Subject Classification

  • 49K20 93C20

Keywords

  • Shape memory alloys, phase transitions, systems of nonlinear PDE's, optimal control, necessary conditions of optimality

DOI

10.20347/WIAS.PREPRINT.259

Abstract

We consider an optimal control problem for first order martensitic phase transitions in a deformation-driven experiment on shape memory alloys. For the resulting system of nonlinear partial differential equations using Falk's Landau-Ginzburg model we show the existence and uniqueness of a classical and a weak solution, respectively. The control problem is stated, and the necessary conditions of optimality are derived.

Appeared in

  • Adv. Math. Sci. Appl. 8, (1998), pp. 299-325

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