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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| Autores principales: | , |
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2013
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00416932_v54_n1_p43_Deleo http://hdl.handle.net/20.500.12110/paper_00416932_v54_n1_p43_Deleo |
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| Sumario: | 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. |
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