## 偏微分方程式セミナー(2015/10/19): Classification of the solutions to the focusing nonlinear Schrödinger equation with a repulsive Dirac delta potential, 戍亥 隆恭 氏

2015年 　 10月 19日 16時 30分 ～ 2015年 　 10月 19日 17時 30分

We consider the focusing nonlinear Schrödinger equation with a repulsive Dirac delta potential in the $L^2$ supercritical case for $H^1$ data. Banica and Visciglia proved that all solutions scatter in the defocusing case. However, in the focusing case, the existence of non-scattering solution is well known. Our aim is to classify the behavior of the solutions by the initial data. In this talk, we prove that the sign of a functional at initial time, which appears naturally from the viewpoint of variational argument, determines whether solutions scatter or blow up if the energy-mass is less than that of the standing wave. This talk is based on a joint work with Masahiro Ikeda in Kyoto university.