Hokkaido Mathematical Journal

SHIMOMURA Akihiro,

Scattering theory for the coupled Klein-Gordon-Schr/"{o}dinger equations in two space dimensions II.

Hokkaido Mathematical Journal, 34 (2005) pp.405-433

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Abstract

We study the scattering theory for the coupled Klein-Gordon-Schr/"{o}dinger equation with the Yukawa type interaction in two space dimensions. The scattering problem for this equation belongs to the borderline between the short range case and the long range one. We show the existence of the wave operators to this equation without any size restriction on the Klein-Gordon component of the final state and any restriction on the support of the Fourier transform of the final state.

MSC(Primary)35Q40
MSC(Secondary)35P25, 35B40
Uncontrolled KeywordsKlein-Gordon-Schr/"{o}dinger equations, scattering theory, wave operators,asymptotic behavior of solutions