Abstract:
We consider an optimal internal control problem for the cubic nonlinear Schrödinger (NLS) equation on the line. We prove well-posedness of the problem and existence of an optimal control. In addition, we show first-order optimality conditions. Also, the paper includes the proof of a smoothing effect for the non-homogeneous NLS, which is necessary to obtain the existence of an optimal control. © 2018, Springer-Verlag London Ltd., part of Springer Nature.
Registro:
Documento: |
Artículo
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Título: | Optimal distributed control problem for cubic nonlinear Schrödinger equation |
Autor: | de la Vega, C.S.F.; Rial, D. |
Filiación: | IMAS–CONICET and Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, C1428EGA, Argentina
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Palabras clave: | Noise immunity; Nonlinear Schrödinger equation; Optical fibers; Optimal control; Nonlinear equations; Optical fibers; Dinger equation; First-order optimality condition; Internal controls; Noise immunity; Non-homogeneous; Optimal controls; Optimal distributed control problem; Smoothing effects; Nonlinear optics |
Año: | 2018
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Volumen: | 30
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Número: | 4
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DOI: |
http://dx.doi.org/10.1007/s00498-018-0222-4 |
Título revista: | Mathematics of Control, Signals, and Systems
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Título revista abreviado: | Math Control Signals Syst
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ISSN: | 09324194
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CODEN: | MCSYE
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09324194_v30_n4_p_delaVega |
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Citas:
---------- APA ----------
de la Vega, C.S.F. & Rial, D.
(2018)
. Optimal distributed control problem for cubic nonlinear Schrödinger equation. Mathematics of Control, Signals, and Systems, 30(4).
http://dx.doi.org/10.1007/s00498-018-0222-4---------- CHICAGO ----------
de la Vega, C.S.F., Rial, D.
"Optimal distributed control problem for cubic nonlinear Schrödinger equation"
. Mathematics of Control, Signals, and Systems 30, no. 4
(2018).
http://dx.doi.org/10.1007/s00498-018-0222-4---------- MLA ----------
de la Vega, C.S.F., Rial, D.
"Optimal distributed control problem for cubic nonlinear Schrödinger equation"
. Mathematics of Control, Signals, and Systems, vol. 30, no. 4, 2018.
http://dx.doi.org/10.1007/s00498-018-0222-4---------- VANCOUVER ----------
de la Vega, C.S.F., Rial, D. Optimal distributed control problem for cubic nonlinear Schrödinger equation. Math Control Signals Syst. 2018;30(4).
http://dx.doi.org/10.1007/s00498-018-0222-4