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October  2009, 23(4): 1313-1325. doi: 10.3934/dcds.2009.23.1313

Remarks on global existence and blowup for damped nonlinear Schrödinger equations

Masahoto Ohta 1, and  Grozdena Todorova 2,

1. 

Department of Mathematics, Saitama University, Saitama 338-8570, Japan
2. 

Department of Mathematics, University of Tennessee, Knoxville, TN 37096-1300

Received  January 2007 Revised  August 2007 Published  November 2008

We consider the Cauchy problem for the damped nonlinear Schrödinger equations, and prove some blowup and global existence results which depend on the size of the damping coefficient. We also discuss the $L^2$ concentration phenomenon of blowup solutions in the critical case.
Keywords: blowup, Global existence, damped nonlinear Schrödinger equation.
Mathematics Subject Classification: Primary: 35Q55; Secondary: 35B40.
Citation: Masahoto Ohta, Grozdena Todorova. Remarks on global existence and blowup for damped nonlinear Schrödinger equations. Discrete & Continuous Dynamical Systems, 2009, 23 (4) : 1313-1325. doi: 10.3934/dcds.2009.23.1313
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