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Semiclassical Analysis for Hartree equation
Journal article   Open access   Peer reviewed

Semiclassical Analysis for Hartree equation

Rémi Carles and Satoshi Masaki
Asymptotic Analysis, Vol.58(4), pp.211-227
2008

Abstract

We justify WKB analysis for Hartree equation in space dimension at least three, in a regime which is supercritical as far as semiclassical analysis is concerned. The main technical remark is that the nonlinear Hartree term can be considered as a semilinear perturbation. This is in contrast with the case of the nonlinear Schrodinger equation with a local nonlinearity, where quasilinear analysis is needed to treat the nonlinearity.
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