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De Leo, M.; Sánchez Fernández De La Vega, C.; Rial, D. "Controllability of schrödinger equation with a nonlocal term" (2014) ESAIM - Control, Optimisation and Calculus of Variations. 20(1):23-41
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Abstract:

This paper is concerned with the internal distributed control problem for the 1D Schrödinger equation, i ut(x,t) =-uxx+α (x) u+m(u) u, that arises in quantum semiconductor models. Here m(u) is a non local Hartree-type nonlinearity stemming from the coupling with the 1D Poisson equation, and α(x) is a regular function with linear growth at infinity, including constant electric fields. By means of both the Hilbert Uniqueness Method and the contraction mapping theorem it is shown that for initial and target states belonging to a suitable small neighborhood of the origin, and for distributed controls supported outside of a fixed compact interval, the model equation is controllable. Moreover, it is shown that, for distributed controls with compact support, the exact controllability problem is not possible. © 2014 EDP Sciences, SMAI.

Registro:

Documento: Artículo
Título:Controllability of schrödinger equation with a nonlocal term
Autor:De Leo, M.; Sánchez Fernández De La Vega, C.; Rial, D.
Filiación:Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, (1613) Los Polvorines, Buenos Aires, Argentina
Universidad de Buenos Aires, Ciudad Universitaria, Departamento de Matemática, Pabellón I (1428) Buenos Aires, Argentina
Palabras clave:Constant electric field; Hartree potential; Internal controllability; Nonlinear Schrödinger-Poisson
Año:2014
Volumen:20
Número:1
Página de inicio:23
Página de fin:41
DOI: http://dx.doi.org/10.1051/cocv/2013052
Título revista:ESAIM - Control, Optimisation and Calculus of Variations
Título revista abreviado:Control Optimisation Calc. Var.
ISSN:12928119
CODEN:ECOVF
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_12928119_v20_n1_p23_DeLeo

Referencias:

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Citas:

---------- APA ----------
De Leo, M., Sánchez Fernández De La Vega, C. & Rial, D. (2014) . Controllability of schrödinger equation with a nonlocal term. ESAIM - Control, Optimisation and Calculus of Variations, 20(1), 23-41.
http://dx.doi.org/10.1051/cocv/2013052
---------- CHICAGO ----------
De Leo, M., Sánchez Fernández De La Vega, C., Rial, D. "Controllability of schrödinger equation with a nonlocal term" . ESAIM - Control, Optimisation and Calculus of Variations 20, no. 1 (2014) : 23-41.
http://dx.doi.org/10.1051/cocv/2013052
---------- MLA ----------
De Leo, M., Sánchez Fernández De La Vega, C., Rial, D. "Controllability of schrödinger equation with a nonlocal term" . ESAIM - Control, Optimisation and Calculus of Variations, vol. 20, no. 1, 2014, pp. 23-41.
http://dx.doi.org/10.1051/cocv/2013052
---------- VANCOUVER ----------
De Leo, M., Sánchez Fernández De La Vega, C., Rial, D. Controllability of schrödinger equation with a nonlocal term. Control Optimisation Calc. Var. 2014;20(1):23-41.
http://dx.doi.org/10.1051/cocv/2013052