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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Detalles Bibliográficos
Publicado: 2018
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:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09324194_v30_n4_p_delaVega
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
Descripción
Sumario: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.

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