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

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2007, 2007(Special): 487-494. doi: 10.3934/proc.2007.2007.487

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

1.	Department of Mathematical Sciences, Faculty of Science, Ehime University, 2-5 Bunkyo-cho, Matsuyama-shi, Ehime, Japan 790-77

Received September 2006 Revised March 2007 Published September 2007

Abstract
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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 SchÂ¨odinger, mixed problem..

Mathematics Subject Classification: Primary: 35B30, 35Q55; Secondary: 81Q9.

Citation: Takahiro Hashimoto. Nonexistence of global solutions of nonlinear Schrodinger equations in non star-shaped domains. Conference Publications, 2007, 2007 (Special) : 487-494. doi: 10.3934/proc.2007.2007.487

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