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Author: Yamazaki, Noriaki ×

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    Lagrange multiplier and singular limit of double obstacle problems for Allen-Cahn equation with constraint
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Farshbaf Shaker, Mohammad Hassan; Takeshi, Takeshi; Yamazaki, Noriaki; Kenmochi, Nobuyuki
    We consider an Allen--Cahn equation with a constraint of double obstacle-type. This constraint is a subdifferential of an indicator function on the closed interval, which is a multivalued function. In this paper we study the properties of the Lagrange multiplier to our equation. Also, we consider the singular limit of our system and clarify the limit of the solution and the Lagrange multiplier to our double obstacle problem. Moreover, we give some numerical experiments of our problem by using the Lagrange multiplier.
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    Singular limit of Allen-Cahn equation with constraints and its Lagrange multiplier
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Farshbaf Shaker, Mohammad Hassan; Fukao, Takeshi; Yamazaki, Noriaki
    We consider the Allen-Cahn equation with constraint. Our constraint is the subdifferential of the indicator function on the closed interval, which is the multivalued function. In this paper we give the characterization of the Lagrange multiplier to our equation. Moreover, we consider the singular limit of our system and clarify the limit of the solution and the Lagrange multiplier to our problem.
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    Optimal 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, Noriaki
    In 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.
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    Optimal 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, Noriaki
    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.