Long Range Scattering and Modified Wave Operators for some Hartree Type Equations
Abstract
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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 1998
 DOI:
 10.48550/arXiv.math/9807031
 arXiv:
 arXiv:math/9807031
 Bibcode:
 1998math......7031G
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 35P25 (Primary) 35B40;
 35Q40;
 81U99 (Secondary)
 EPrint:
 TeX, 89 pages, available http://qcd.th.upsud.fr