Abstract:
We study an optimal control problem for the Schrödinger equation with a real-valued factor in its nonlinear part where the control function is square summable and the quality criterion is Lions' functional. First, we examine the correctness of the statement of the reduced problem and, second, we do that of the optimal control problem. We also study the differentiability of Lions' functional and obtain a necessary optimality condition in the form of a variational inequality.
Citation:
N. M. Mahmudov, “An optimal control problem for the Schrödinger equation with a real-valued factor”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 11, 31–40; Russian Math. (Iz. VUZ), 54:11 (2010), 27–35
\Bibitem{Mah10}
\by N.~M.~Mahmudov
\paper An optimal control problem for the Schr\"odinger equation with a~real-valued factor
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 11
\pages 31--40
\mathnet{http://mi.mathnet.ru/ivm7148}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2814562}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 11
\pages 27--35
\crossref{https://doi.org/10.3103/S1066369X10110034}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649580134}
Linking options:
https://www.mathnet.ru/eng/ivm7148
https://www.mathnet.ru/eng/ivm/y2010/i11/p31
This publication is cited in the following 4 articles:
Kuecuek G.D., Yagub G., Celik E., “on the Existence and Uniqueness of the Solution of An Optimal Control Problem For Schrodinger Equation”, Discret. Contin. Dyn. Syst.-Ser. S, 12:3 (2019), 503–512
Aksoy N.Y., “Variational Method For the Solution of An Inverse Problem”, J. Comput. Appl. Math., 312 (2017), 82–93
Aksoy N.Y., “the Variational Formulation of An Inverse Problem For Multidimensional Nonlinear Time-Dependent Schrodinger Equation”, J. Inverse Ill-Posed Probl., 24:5 (2016), 559–571
Aksoy N.Y., Aksoy E., Kocak Yu., “An Optimal Control Problem With Final Observation For Systems Governed By Nonlinear Schrodinger Equation”, Filomat, 30:3 (2016), 649–665
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