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Author: Colli, Pierluigi × Author: Yamazaki, Noriaki × End date: 2024 × Start date: 2020 × Type: report × Version: publishedVersion ×

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    Optimal control for shape memory alloys of the one-dimensional Frémond model
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Colli, Pierluigi; Farshbaf Shaker, Mohammad Hassan; Shirakawa, Ken; Yamazaki, Noriaki
    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.