Artículo
De leo, M.; De la vega, C.S.F.; Rial, D. "Global controllability of the 1D schrödinger-poisson equation" (2013) Revista de la Union Matematica Argentina. 54(1):43-54
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Abstract:
This paper is concerned with both the local and global internal controllability of the 1D Schrödinger-Poisson equation i ut(x, t) = -uxx + V (u) u; which arises in quantum semiconductor models. Here V (u) is a Hartree-type nonlinearity stemming from the coupling with the 1D Poisson equation, which includes the so-called doping prolle or impurities. More precisely, it is shown that for both attractive and repulsive self-consistent potentials depending on the balance between the total charge and the impurities this problem is globally internal controllable in a suitable Sobolev space.
Registro:
| Documento: | Artículo |
| Título: | Global controllability of the 1D schrödinger-poisson equation |
| Autor: | De leo, M.; De la vega, C.S.F.; Rial, D. |
| Filiación: | Instituto de Ciencias, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, (1613) Los Polvorines, Buenos Aires, Argentina IMAS-CONICET and Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, 1428 Buenos Aires, Argentina |
| Palabras clave: | Doping prole; Hartree potential; Internal controllability; Nonlinear Schrödinger-Poisson |
| Año: | 2013 |
| Volumen: | 54 |
| Número: | 1 |
| Página de inicio: | 43 |
| Página de fin: | 54 |
| Título revista: | Revista de la Union Matematica Argentina |
| Título revista abreviado: | Rev. Union Mat. Argent. |
| ISSN: | 00416932 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v54_n1_p43_Deleo |
Referencias:
- Cazenave, T., Haraux, A., An Introduction to Semilinear Evolution Equations (1998), Oxford University Press; De Leo, M., Rial, D., Well-posedness and smoothing effect of Schrödinger-Poisson equation (2007) J. Math. Phys, 48, p. 15. , 093509-1
- Harkness, G.K., Oppo, G.L., Benkler, E., Kreuzer, M., Neubecker, R., Tschudi, T., Fourier space control in an LCLV feedback system (1999), 1, pp. 177-182. , Journal of Optics B: Quantum and Semiclassical Optics; Illner, R., Lange, H., Teisman, H., A note on the exact internal control of nonlinear Schröodinger equations. In: Quantum Control: Mathematical and Numerical Challenges (2003) Amer. Math. Soc, pp. 127-137. , CRM Proceedings and Lectures Notes, 33
- Illner, R., Lange, H., Teisman, H., Limitations on the control of Schröodinger equations (2006) ESAIM Control Optim. Calc. Var., 12, pp. 615-635
- Markowich, P., Ringhofer, C., Schmeiser, C., Semiconductor equations, Springer, Vienna (1990); McDonald, G.S., Firth, W.J., Spatial solitary-wave optical memory (1990) J. Optical Society America B, 7, pp. 1328-1335
- Reed, M., Simon, B., Methods of Modern Mathematical Physics (1975), 2. , Fourier Analysis, Self-Adjointness, Academic Press; Rosier, L., Zhang, B., Exact boundary controllability of the nonlinear Schröodinger equation (2009) J. Differential Equations, 246, pp. 4129-4153
- Zuazua, E., Remarks on the controllability of the Schröodinger equation. In: Quantum Control: Mathematical and Numerical Challenges (2003) Amer. Math. Soc., pp. 193-211. , CRM Proceedings and Lectures Notes, 33
Citas:
---------- APA ----------
De leo, M., De la vega, C.S.F. & Rial, D. (2013) . Global controllability of the 1D schrödinger-poisson equation. Revista de la Union Matematica Argentina, 54(1), 43-54.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v54_n1_p43_Deleo [ ]
---------- CHICAGO ----------
De leo, M., De la vega, C.S.F., Rial, D. "Global controllability of the 1D schrödinger-poisson equation" . Revista de la Union Matematica Argentina 54, no. 1 (2013) : 43-54.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v54_n1_p43_Deleo [ ]
---------- MLA ----------
De leo, M., De la vega, C.S.F., Rial, D. "Global controllability of the 1D schrödinger-poisson equation" . Revista de la Union Matematica Argentina, vol. 54, no. 1, 2013, pp. 43-54.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v54_n1_p43_Deleo [ ]
---------- VANCOUVER ----------
De leo, M., De la vega, C.S.F., Rial, D. Global controllability of the 1D schrödinger-poisson equation. Rev. Union Mat. Argent. 2013;54(1):43-54.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v54_n1_p43_Deleo [ ]
