Nonexistence of global solutions of nonlinear Schrodinger equations in non star-shaped domains

Pages: 487 - 494, Issue Special, September 2007

 Abstract        Full Text (178.7K)              

Takahiro Hashimoto - Department of Mathematical Sciences, Faculty of Science, Ehime University, 2-5 Bunkyo-cho, Matsuyama-shi, Ehime, Japan 790-77, Japan (email)

Abstract: In this paper, we discuss the nonexistence of global solutions of mixed problems of the nonlinear Schödinger equations with power nonlinearity. When the domain is whole space, there are many results concerning the nonexistence of global solutions ( or existence of blow-up solutions ) for the equation. For the case of a general domain, there are few studies of blowing-up conditions. The main purpose of this paper is to discuss the nonexistence of global solutions in a deformed tube-shaped domain which is not star-shaped.

Keywords:  Blow-up, nonlinear Sch¨odinger, mixed problem.
Mathematics Subject Classification:  Primary: 35B30, 35Q55; Secondary: 81Q99.

Received: September 2006;      Revised: March 2007;      Published: September 2007.