Optimal control for shape memory alloys of the one-dimensional Frémond model
- Colli, Pierluigi
- Farshbaf Shaker, Mohammad Hassan
- Shirakawa, Ken
- Yamazaki, Noriaki
2010 Mathematics Subject Classification
- 49J20 35K55 35R35
- Optimal control problem, one-dimensional Frémond model, shape memory alloys, Mosco convergence, subdifferentials
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.
- Numer. Funct. Anal. Optim., 41 (2020), pp. 1421-1471, DOI 10.1080/01630563.2020.1774892 .