Differential and Integral Equations

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

Hironobu Sasaki

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Abstract

We consider the scattering problem 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.

Article information

Source
Differential Integral Equations, Volume 19, Number 8 (2006), 877-889.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356050339

Mathematical Reviews number (MathSciNet)
MR2263433

Zentralblatt MATH identifier
1212.35338

Subjects
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35P25: Scattering theory [See also 47A40]

Citation

Sasaki, Hironobu. Convergence of scattering operators for the Klein-Gordon equation with a nonlocal nonlinearity. Differential Integral Equations 19 (2006), no. 8, 877--889. https://projecteuclid.org/euclid.die/1356050339


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