This paper is concerned with the derivation of uniform bounds with respect to the scaled Planck constant ${\cal E}$ for solutions to the open transient Schrödinger-Poisson system introduced by Ben Abdallah et al in [Math.Meth.Mod. in App. Sci., 15, 667-688, 2005]. The uniform estimates stem from a careful analysis of the non-local in time transparent boundary conditions which allow to restrict the original problem posed on an unbounded domain to a bounded domain of interest. These bounds can be used to obtain the semi-classical limit of the system. The paper also gives an existence and uniqueness result for weak solutions while they were previously defined in a strong sense.
Publié le : 2007-09-15
Classification:
semiconductors,
non-linear Schrödinger equation,
open boundary conditions,
uniform estimates,
35Q40,
35Q55
@article{1188405675,
author = {Pinaud, Olivier},
title = {Uniform bounds and weak solutions to an open Schr\"odinger-Poisson system},
journal = {Commun. Math. Sci.},
volume = {5},
number = {1},
year = {2007},
pages = { 697-722},
language = {en},
url = {http://dml.mathdoc.fr/item/1188405675}
}
Pinaud, Olivier. Uniform bounds and weak solutions to an open Schrödinger-Poisson system. Commun. Math. Sci., Tome 5 (2007) no. 1, pp. 697-722. http://gdmltest.u-ga.fr/item/1188405675/