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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
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
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
Volumen:30
Número:4
DOI: http://dx.doi.org/10.1007/s00498-018-0222-4
Título revista:Mathematics of Control, Signals, and Systems
Título revista abreviado:Math Control Signals Syst
ISSN:09324194
CODEN:MCSYE
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