Global controllability of the 1D schrödinger-poisson equation
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 i...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00416932_v54_n1_p43_Deleo |
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todo:paper_00416932_v54_n1_p43_Deleo2023-10-03T14:51:20Z Global controllability of the 1D schrödinger-poisson equation De leo, M. De la vega, C.S.F. Rial, D. Doping prole Hartree potential Internal controllability Nonlinear Schrödinger-Poisson 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. Fil:De leo, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rial, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00416932_v54_n1_p43_Deleo |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Doping prole Hartree potential Internal controllability Nonlinear Schrödinger-Poisson |
| spellingShingle |
Doping prole Hartree potential Internal controllability Nonlinear Schrödinger-Poisson De leo, M. De la vega, C.S.F. Rial, D. Global controllability of the 1D schrödinger-poisson equation |
| topic_facet |
Doping prole Hartree potential Internal controllability Nonlinear Schrödinger-Poisson |
| description |
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. |
| format |
JOUR |
| author |
De leo, M. De la vega, C.S.F. Rial, D. |
| author_facet |
De leo, M. De la vega, C.S.F. Rial, D. |
| author_sort |
De leo, M. |
| title |
Global controllability of the 1D schrödinger-poisson equation |
| title_short |
Global controllability of the 1D schrödinger-poisson equation |
| title_full |
Global controllability of the 1D schrödinger-poisson equation |
| title_fullStr |
Global controllability of the 1D schrödinger-poisson equation |
| title_full_unstemmed |
Global controllability of the 1D schrödinger-poisson equation |
| title_sort |
global controllability of the 1d schrödinger-poisson equation |
| url |
http://hdl.handle.net/20.500.12110/paper_00416932_v54_n1_p43_Deleo |
| work_keys_str_mv |
AT deleom globalcontrollabilityofthe1dschrodingerpoissonequation AT delavegacsf globalcontrollabilityofthe1dschrodingerpoissonequation AT riald globalcontrollabilityofthe1dschrodingerpoissonequation |
| _version_ |
1807316837622349824 |