LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL

doi:10.1016/S0252-9602(12)60090-3

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (3): 1181-1192.doi: 10.1016/S0252-9602(12)60090-3

LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL

朱世辉|张健

1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China；
2. Visual Computing and Virtual Reality Key Laboratory, Sichuan Normal University, Chengdu 610066, China

收稿日期:2010-10-27 出版日期:2012-05-20 发布日期:2012-05-20
基金资助:
Supported by National Science Foundation of China (11071177) and Excellent Youth Foundation of Sichuan Province (2012JQ0011).

LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL

ZHU Shi-Hui, ZHANG Jian

1. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, China；
2. Visual Computing and Virtual Reality Key Laboratory, Sichuan Normal University, Chengdu 610066, China

Received:2010-10-27 Online:2012-05-20 Published:2012-05-20
Supported by:
Supported by National Science Foundation of China (11071177) and Excellent Youth Foundation of Sichuan Province (2012JQ0011).

摘要/Abstract

摘要：

This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear Schr¨odinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the limiting behavior of blow-up solutions with critical and small super-critical mass are obtained in the natural energy space ∑ ={u ∈ H¹; ∫_RN |x|²|u|²dx < +∞}. Moreover, an interesting concentration property of the blow-up solutions with critical mass is gotten, which reads that |u(t, x)|² → ||Q||² _L2 δ_x_=x1 as t → T.

关键词: Nonlinear Schr¨odinger equation, Stark potential, blow-up solution, limiting behavior, mass concentration

Abstract:

Key words: Nonlinear Schr¨odinger equation, Stark potential, blow-up solution, limiting behavior, mass concentration

中图分类号:

35Q55

朱世辉, 张健. LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL[J]. 数学物理学报(英文版), 2012, 32(3): 1181-1192.

ZHU Shi-Hui, ZHANG Jian. LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL[J]. Acta mathematica scientia,Series B, 2012, 32(3): 1181-1192.

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LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL

LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL

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