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Mathematical Control and Related Fields (MCRF)
 

Rate of $L^2$-concentration of the blow-up solution for critical nonlinear Schrödinger equation with potential

Pages: 119 - 127, Volume 1, Issue 1, March 2011      doi:10.3934/mcrf.2011.1.119

 
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Jian Zhang - College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, China (email)
Shihui Zhu - College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China (email)
Xiaoguang Li - College of Economics, Sichuan Normal University, Chengdu 610066, China (email)

Abstract: We consider the blow-up solutions of the Cauchy problem for the critical nonlinear Schrödinger equation with a repulsive harmonic potential. In terms of Merle and Tsutsumi's arguments as well as Carles' transform, the $L^2$-concentration property of radially symmetric blow-up solutions is obtained.

Keywords:  Nonlinear Schrödinger equation, repulsive harmonic potential, blow-up solution, $L^2$-concentration.
Mathematics Subject Classification:  Primary: 35Q55; Secondary: 35B44.

Received: October 2010;      Revised: January 2011;      Available Online: March 2011.

 References