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

2006-06-05 16:30 - 2006-06-05 17:30
Faculty of Science Building #8 Room 309
Hironobu Sasaki (Hokkaido Univ.)
We consider the scattering problems for two types of nonlinearKlein-Gordon equations. One is the equation of the Hartree type,and the other one is the equation with power nonlinearity.In this talk, we show that the scattering operator for the equationof the Hartree type converges to that for the one with powernonlinearity in some sense. Our proof is based on some inequalitiesin the Lorentz space, and a strong limit of Riesz potentials.