Optimal Control for Shape Memory Alloys of the One-Dimensional Frémond Model. (9th September 2020) - Colli, Pierluigi; Hassan Farshbaf-Shaker, M.; Shirakawa, Ken; Yamazaki, Noriaki
Abstract: In this article, 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.