Optimal Control of Martensitic Phase Transitions in a Deformation-Driven Experiment on Shape Memory Alloys
- Bubner, Nikolaus
- Sprekels, Jürgen
2010 Mathematics Subject Classification
- 49K20 93C20
- Shape memory alloys, phase transitions, systems of nonlinear PDE's, optimal control, necessary conditions of optimality
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.
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