PDE Seminar (2015/10/19): Classification of the solutions to the focusing nonlinear Schrödinger equation with a repulsive Dirac delta potential
 Date

20151019 16:30 
20151019 17:30
 Place
 Faculty of Science Building #3, Room 309

Speaker/Organizer
 Takahisa Inui (Kyoto University)

 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 nonscattering 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 energymass is less than that of the standing wave. This talk is based on a joint work with Masahiro Ikeda in Kyoto university.