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Scattering theory for the Dirac equation with a non-local term

Published online by Cambridge University Press:  08 July 2009

Shuji Machihara  and
Kimitoshi Tsutaya
Shuji Machihara
Affiliation:
Department of Mathematics, Faculty of Education, Saitama University, 255 Shimo-Okubo, Sakura-ku, Saitama City 338-8570, Japan (matihara@math.edu.saitama-u.ac.jp)
Kimitoshi Tsutaya
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan (tsutaya@math.sci.hokudai.ac.jp)
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Abstract

Consider a scattering problem for the Dirac equation with a non-local term including the Hartree type, say the cubic convolution term. We show the existence of scattering operators for small initial data in the subcritical and critical Sobolev spaces.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 139 , Issue 4 , August 2009 , pp. 867 - 878
Copyright
Copyright © Royal Society of Edinburgh 2009

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