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- ItemOptimal control of doubly nonlinear evolution equations governed by subdifferentials without uniqueness of solutions(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Farshbaf-Shaker, M. Hassan; Yamazaki, NoriakiIn this paper we study an optimal control problem for a doubly nonlinear evolution equation governed by time-dependent subdifferentials. We prove the existence of solutions to our equation. Also, we consider an optimal control problem without uniqueness of solutions to the state system. Then, we prove the existence of an optimal control which minimizes the nonlinear cost functional. Moreover, we apply our general result to some model problem.
- ItemOptimal 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, NoriakiIn 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.