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September 2007 Uniform bounds and weak solutions to an open Schrödinger-Poisson system
Olivier Pinaud
Commun. Math. Sci. 5(3): 697-722 (September 2007).


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.


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Olivier Pinaud. "Uniform bounds and weak solutions to an open Schrödinger-Poisson system." Commun. Math. Sci. 5 (3) 697 - 722, September 2007.


Published: September 2007
First available in Project Euclid: 29 August 2007

zbMATH: 1135.35078
MathSciNet: MR2352338

Primary: 35Q40 , 35Q55

Keywords: non-linear Schrödinger equation , open boundary conditions , semiconductors , uniform estimates

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 3 • September 2007
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