Dept. Math, Hokkaido Univ. EPrints Server

Convergence of scattering operators for the Klein-Gordon equation with a nonlocal nonlinearity

Preprint Series # 786
Sasaki, Hironobu Convergence of scattering operators for the Klein-Gordon equation with a nonlocal nonlinearity. (2006);

[img]PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
150Kb

Abstract

We consider the scattering problems for two types of nonlinear Klein-Gordon equations. One is the equation of the Hartree type, and the other one is the equation with power nonlinearity. We show that the scattering operator for the equation of the Hartree type converges to that for the one with power nonlinearity in some sense. Our proof is based on some inequalities in the Lorentz space, and a strong limit of Riesz potentials.

Item Type:Preprint
Subjects:35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:1539