Differential and Integral Equations
- Differential Integral Equations
- Volume 19, Number 8 (2006), 877-889.
Convergence of scattering operators for the Klein-Gordon equation with a nonlocal nonlinearity
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.
Differential Integral Equations, Volume 19, Number 8 (2006), 877-889.
First available in Project Euclid: 21 December 2012
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35L70: Nonlinear second-order hyperbolic equations
Secondary: 35P25: Scattering theory [See also 47A40]
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