August  2006, 15(3): 973-981. doi: 10.3934/dcds.2006.15.973

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

1. 

Department of Mathematics, Hokkaido University, 060-0810, Japan

Received  July 2005 Revised  January 2006 Published  April 2006

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.
Citation: Hironobu Sasaki. Small data scattering for the Klein-Gordon equation with cubic convolution nonlinearity. Discrete & Continuous Dynamical Systems - A, 2006, 15 (3) : 973-981. doi: 10.3934/dcds.2006.15.973
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