Convergence of scattering operators for the KleinGordon equation with a nonlocal nonlinearityPreprint Series # 786
AbstractWe consider the scattering problems for two types of nonlinear KleinGordon 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.
