Long Range Scattering and Modified Wave Operators for some Hartree Type Equations

Details Long Range Scattering and Modified Wave Operators for some Hartree Type Equations Long Range Scattering and Modified Wave Operators for some Hartree Type Equations

1998-07-07

arxiv.org/abs/math/9807031v1

Mathematics

Analysis of PDEs

TeX, 89 pages, available http://qcd.th.u-psud.fr

Scientific paper

We study the theory of scattering for a class of Hartree type equations with long range interactions in space dimension n > 2, including Hartree equations with potential V(x) = lambda |x|^{- gamma} with gamma < 1. For 1/2 < gamma < 1 we prove the existence of modified wave operators with no size restriction on the data and we determine the asymptotic behaviour in time of solutions in the range of the wave operators.

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