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

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Date
2020
Volume
2737
Issue
Journal
Series Titel
WIAS Preprints
Book Title
Publisher
Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract

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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Citation
Colli, P., Farshbaf Shaker, M. H., Shirakawa, K., & Yamazaki, N. (2020). Optimal control for shape memory alloys of the one-dimensional Frémond model (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik. https://doi.org//10.20347/WIAS.PREPRINT.2737
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