Artículo
Controllability of Schrödinger equation with a nonlocal term
Fecha de publicación:
08/2013
Editorial:
EDP Sciences
Revista:
ESAIM-Control Optimisation and Calculus of Variations
ISSN:
1262-3377
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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.
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Articulos(IMAS)
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos de INSTITUTO DE INVESTIGACIONES MATEMATICAS "LUIS A. SANTALO"
Articulos(SEDE CENTRAL)
Articulos de SEDE CENTRAL
Articulos de SEDE CENTRAL
Citación
Rial, Diego Fernando; Sanchez Fernandez de la Vega, Constanza Mariel; de Leo, Mariano Fernando; Controllability of Schrödinger equation with a nonlocal term; EDP Sciences; ESAIM-Control Optimisation and Calculus of Variations; 20; 1; 8-2013; 23-41
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