Optimal distributed control problem for cubic nonlinear Schrödinger equation

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...

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Autores principales: de la Vega, C.S.F., Rial, D.
Formato: JOUR
Materias:
Noise immunity
Nonlinear Schrödinger equation
Optical fibers
Optimal control
Nonlinear equations
Dinger equation
First-order optimality condition
Internal controls
Non-homogeneous
Optimal controls
Optimal distributed control problem
Smoothing effects
Nonlinear optics
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_09324194_v30_n4_p_delaVega
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_09324194_v30_n4_p_delaVega
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spelling todo:paper_09324194_v30_n4_p_delaVega2023-10-03T15:48:32Z Optimal distributed control problem for cubic nonlinear Schrödinger equation de la Vega, C.S.F. Rial, D. 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 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_09324194_v30_n4_p_delaVega
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic 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
spellingShingle 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
de la Vega, C.S.F.
Rial, D.
Optimal distributed control problem for cubic nonlinear Schrödinger equation
topic_facet 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
description 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.
format JOUR
author de la Vega, C.S.F.
Rial, D.
author_facet de la Vega, C.S.F.
Rial, D.
author_sort de la Vega, C.S.F.
title Optimal distributed control problem for cubic nonlinear Schrödinger equation
title_short Optimal distributed control problem for cubic nonlinear Schrödinger equation
title_full Optimal distributed control problem for cubic nonlinear Schrödinger equation
title_fullStr Optimal distributed control problem for cubic nonlinear Schrödinger equation
title_full_unstemmed Optimal distributed control problem for cubic nonlinear Schrödinger equation
title_sort optimal distributed control problem for cubic nonlinear schrödinger equation
url http://hdl.handle.net/20.500.12110/paper_09324194_v30_n4_p_delaVega
work_keys_str_mv AT delavegacsf optimaldistributedcontrolproblemforcubicnonlinearschrodingerequation
AT riald optimaldistributedcontrolproblemforcubicnonlinearschrodingerequation
_version_ 1807315748574461952

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