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Author: Farshbaf-Shaker, M. Hassan × End date: 2019 × Start date: 2010 × Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik × Subject: optimality conditions ×

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    Optimal control of Allen-Cahn systems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Blank, Luise; Farshbaf-Shaker, M. Hassan; Hecht, Claudia; Michl, Josef; Rupprecht, Christoph
    Optimization problems governed by Allen-Cahn systems including elastic effects are formulated and first-order necessary optimality conditions are presented. Smooth as well as obstacle potentials are considered, where the latter leads to an MPEC. Numerically, for smooth potential the problem is solved efficiently by the Trust-Region-Newton-Steihaug-cg method. In case of an obstacle potential first numerical results are presented.
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    A deep quench approach to the optimal control of an Allen-Cahn equation with dynamic boundary conditions and double obstacles
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Colli, Pierluigi; Farshbaf-Shaker, M. Hassan; Sprekels, Jürgen
    In this paper, we investigate optimal control problems for Allen-Cahn variational inequalities with a dynamic boundary condition involving double obstacle potentials and the Laplace-Beltrami operator. The approach covers both the cases of distributed controls and of boundary controls. The cost functional is of standard tracking type, and box constraints for the controls are prescribed. We prove existence of optimal controls and derive first-order necessary conditions of optimality. The general strategy is the following: we use the results that were recently established by two of the authors in the paper [5] for the case of (differentiable) logarithmic potentials and perform a so-called deep quench limit. Using compactness and monotonicity arguments, it is shown that this strategy leads to the desired first-order necessary optimality conditions for the case of (non-differentiable) double obstacle potentials.