Type: Article

Blow up of solutions to nonlinear Neumann boundary value problem for Schrödinger equations

Hayashi, Nakao; Kaikina, Elena I.; Naumkin, Pavel I.; Ogawa, Takayosh;

Abstract:

Our purpose is to consider the life span of solutions to the nonlinear Neumann boundary value problem for one dimensional nonlinear Schrödinger equation on a half-line ?????i?tu+12?2xu=0,t>0,x?R+,u(0,x)=u0(x),x?R+,??xu(t,0)=g(t,0),t>0, where g(t,0)=e??4i|u(t,0)|q. We prove that for any q>2, and r>2(q?1), there exists an initial function u0??H?(2r?12)x such that the maximal existence time is finite.