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Long range scattering and modified wave operators for Hartree equations. (English) Zbl 1067.35501
Journées “Équations aux dérivées partielles”, Saint-Jean-de-Monts, France, 31 mai au 4 juin 1999. Exposés Nos. I–XIX. Nantes: Université de Nantes. Exp. No. XVII, 9 p. (1999).
Summary: We study the theory of scattering for the Hartree equation with long-range potentials. 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.
See also [Rev. Math. Phys. 12, No. 3, 361-429 (2000; Zbl 1044.35041); Ann. Henri Poincaré 1, No. 4, 753–800 (2000; Zbl 1024.35084); J. Differ. Equations 175, No. 2, 415–501 (2001; Zbl 0991.35057)].
For the entire collection see [Zbl 0990.00047].
MSC:
35P25 Scattering theory for PDEs
35Q40 PDEs in connection with quantum mechanics
81U99 Quantum scattering theory
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