Hokkaido Mathematical Journal

Scattering theory for the coupled Klein-Gordon-Schrödinger equations in two space dimensions II

Akihiro SHIMOMURA

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Abstract

We study the scattering theory for the coupled Klein-Gordon-Schrödinger 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.

Article information

Source
Hokkaido Math. J., Volume 34, Number 2 (2005), 405-433.

Dates
First available in Project Euclid: 29 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1285766230

Digital Object Identifier
doi:10.14492/hokmj/1285766230

Mathematical Reviews number (MathSciNet)
MR2159005

Zentralblatt MATH identifier
1090.35130

Subjects
Primary: 35Q40: PDEs in connection with quantum mechanics
Secondary: 35P25: Scattering theory [See also 47A40] 35B40: Asymptotic behavior of solutions

Keywords
Klein-Gordon-Schrödinger equations scattering theory wave operators,asymptotic behavior of solutions

Citation

SHIMOMURA, Akihiro. Scattering theory for the coupled Klein-Gordon-Schrödinger equations in two space dimensions II. Hokkaido Math. J. 34 (2005), no. 2, 405--433. doi:10.14492/hokmj/1285766230. https://projecteuclid.org/euclid.hokmj/1285766230


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