Optimal Control for Shape Memory Alloys of the One-Dimensional Frémond Model. (9th September 2020)

• Record Type: Journal Article
• Authors: Colli, Pierluigi; Hassan Farshbaf-Shaker, M.; Shirakawa, Ken; Yamazaki, Noriaki
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 12(2020)
• Page Start: 1421
• Page End: 1471
• Publication Date: 2020-09-09
• Subjects: One-dimensional Frémond model -- optimal control problem -- shape memory alloys -- subdifferentials; 49J20 -- 35K55 -- 35R35; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2020.1774892
• Languages: English
• ISSNs: 0163-0563

Abstract

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.