Controllability of schrödinger equation with a nonlocal term
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...
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2014
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| Acceso en línea: | Registro en Scopus DOI Handle Registro en la Biblioteca Digital |
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| 003 | AR-BaUEN | ||
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| 008 | 190411s2014 xx ||||fo|||| 00| 0 eng|d | ||
| 024 | 7 | |2 scopus |a 2-s2.0-84893978200 | |
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| 100 | 1 | |a De Leo, M. | |
| 245 | 1 | 0 | |a Controllability of schrödinger equation with a nonlocal term |
| 260 | |c 2014 | ||
| 270 | 1 | 0 | |m Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, (1613) Los Polvorines, Buenos Aires, Argentina |
| 506 | |2 openaire |e Política editorial | ||
| 504 | |a Cazenave, T., Semilinear Schrödinger?equations (2003) AMS | ||
| 504 | |a De Leo, M., On the existence of ground states for nonlinear Schrödinger-Poisson equation (2010) Nonlinear Anal., 73, pp. 979-986 | ||
| 504 | |a De Leo, M., Rial, D., Well-posedness and smoothing effect of nonlinear Schrödinger-Poisson equation (2007) J. Math. Phys., 48, pp. 093509-094115 | ||
| 504 | |a Harkness, G.K., Oppo, G.-L., Benkler, E., Kreuzer, M., Neubecker, R., Tschudi, T., Fourier space control in an LCLV feedback system (1999) Journal of Optics B: Quantum and Semiclassical Optics, 1 (1), pp. 177-182. , PII S1464426699960123 | ||
| 504 | |a Illner, R., Lange, H., Teismann, H., A note on 33 of the exact internal control of nonlinear schrödinger?Equations (2003) Quantum Control: Mathematical and Numerical Challenges, 33, pp. 127-136. , CRM Proc. Lect. Notes | ||
| 504 | |a Illner, R., Lange, H., Teismann, H., Limitations on the control of schrödinger equations (2006) ESAIM: COCV, 12, pp. 615-635 | ||
| 504 | |a Kato, T., (1995) Perturbation Theory for Linear Operators, , Springer | ||
| 504 | |a Markowich, P., Ringhofer, C., Schmeiser, C., (1990) Semiconductor Equations, , Springer, Vienna | ||
| 504 | |a McDonald, G.S., Firth, W.J., Spatial solitary-wave optical memory (1990) J. Optical Soc. America B, 7, pp. 1328-1335 | ||
| 504 | |a Reed, M., Simon, B., Methods of modern math. Phys (1975) Fourier Analysis, Self-Adjointness, 2. , Academic Press | ||
| 504 | |a Rosier, L., Zhang, B., Exact boundary controllability of the nonlinear Schrödinger equation (2009) J. Differ. Equ., 246, pp. 4129-4153 | ||
| 504 | |a Simon, B., Phase space analysis of simple scattering systems: Extensions of some work of Enss (1979) Duke Math. J., 46, pp. 119-168 | ||
| 504 | |a Zuazua, E., Remarks on the controllability of the Schrödinger?equation (2003) Quantum Control: Mathematical and Numerical Challenges, 33, pp. 193-211. , CRM Proc. Lect. Notes | ||
| 520 | 3 | |a 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. |l eng | |
| 593 | |a Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, (1613) Los Polvorines, Buenos Aires, Argentina | ||
| 593 | |a Universidad de Buenos Aires, Ciudad Universitaria, Departamento de Matemática, Pabellón I (1428) Buenos Aires, Argentina | ||
| 690 | 1 | 0 | |a CONSTANT ELECTRIC FIELD |
| 690 | 1 | 0 | |a HARTREE POTENTIAL |
| 690 | 1 | 0 | |a INTERNAL CONTROLLABILITY |
| 690 | 1 | 0 | |a NONLINEAR SCHRÖDINGER-POISSON |
| 700 | 1 | |a Sánchez Fernández De La Vega, C. | |
| 700 | 1 | |a Rial, D. | |
| 773 | 0 | |d 2014 |g v. 20 |h pp. 23-41 |k n. 1 |p Control Optimisation Calc. Var. |x 12928119 |t ESAIM - Control, Optimisation and Calculus of Variations | |
| 856 | 4 | 1 | |u https://www.scopus.com/inward/record.uri?eid=2-s2.0-84893978200&doi=10.1051%2fcocv%2f2013052&partnerID=40&md5=0e94016ce9ff70e1f058fee9ad9b9b5e |y Registro en Scopus |
| 856 | 4 | 0 | |u https://doi.org/10.1051/cocv/2013052 |y DOI |
| 856 | 4 | 0 | |u https://hdl.handle.net/20.500.12110/paper_12928119_v20_n1_p23_DeLeo |y Handle |
| 856 | 4 | 0 | |u https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_12928119_v20_n1_p23_DeLeo |y Registro en la Biblioteca Digital |
| 961 | |a paper_12928119_v20_n1_p23_DeLeo |b paper |c PE | ||
| 962 | |a info:eu-repo/semantics/article |a info:ar-repo/semantics/artículo |b info:eu-repo/semantics/publishedVersion | ||
| 999 | |c 75550 | ||