Small data scattering for the Klein-Gordon equation with cubic convolution nonlinearity

Hironobu Sasaki

doi:10.3934/dcds.2006.15.973

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2006, Volume 15, Issue 3: 973-981. Doi: 10.3934/dcds.2006.15.973

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Small data scattering for the Klein-Gordon equation with cubic convolution nonlinearity

Hironobu Sasaki^1,

1.
Department of Mathematics, Hokkaido University, 060-0810

Received: July 2005

Revised: January 2006

Published online: April 2006

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Abstract

We consider the scattering problem for the Klein-Gordon equation with cubic convolution nonlinearity. We give some estimates for the nonlinearity, and prove the existence of the scattering operator, which improves the known results in some sense. Our proof is based on the Strichartz estimates for the inhomogeneous Klein-Gordon equation.

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Mathematics Subject Classification: Primary: 35P25, 81Q05; Secondary: 35B05.

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