The limit equation for the Gross-Pitaevskii equations and S. Terracini's conjecture

被引：65

作者：

Dancer, E. N. ^{[2
]}

Wang, Kelei ^{[2
]}

Zhang, Zhitao ^{[1
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China

[2] Univ Sydney, Sch Math & Stat, Sydney, NSW 2006, Australia

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2012年 / 262卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

Gross-Pitaevskii equation; Singular perturbation; Free boundary problem; Partial regularity; Monotonicity formula; SPATIAL SEGREGATION; SYSTEMS; CONTINUATION; COMPETITION; DYNAMICS; THEOREM;

D O I：

10.1016/j.jfa.2011.10.013

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish the limit system for the Gross-Pitaevskii equations when the segregation phenomenon appears, and shows this Omit is the one arising from the competing systems in population dynamics. This covers and verifies a conjecture of S. Terracini et al., both in the parabolic case and the elliptic case. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：1087 / 1131

页数：45

共 19 条

[1]

[Anonymous], 2006, Applicable Analysis

[2] Singularly perturbed elliptic systems and multi-valued harmonic functions with free boundaries [J].

Caffarelli, L. A. ;

Lin, Fang-Hua .

JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 21 (03) :847-862

[3] The geometry of solutions to a segregation problem for nondivergence systems [J].

Caffarelli, L. A. ;

Karakhanyan, A. L. ;

Lin, Fang-Hua .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2009, 5 (02) :319-351

[4]

CAFFARELLI LA, 2005, GRAD STUD MATH AM MA, V68

[5] NONLOCAL HEAT FLOWS PRESERVING THE L2 ENERGY [J].

Caffarelli, Luis ;

Lin, Fanghua .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2009, 23 (1-2) :49-64

[6] A strong unique continuation theorem for parabolic equations [J].

Chen, XY .

MATHEMATISCHE ANNALEN, 1998, 311 (04) :603-630

[7] Asymptotic estimates for the spatial segregation of competitive systems [J].

Conti, M ;

Terracini, S ;

Verzini, G .

ADVANCES IN MATHEMATICS, 2005, 195 (02) :524-560

[8] A variational problem for the spatial segregation of reaction-diffusion systems [J].

Conti, M ;

Terracini, S ;

Verzini, G .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2005, 54 (03) :779-815

[9]

Dancer EN, 2012, T AM MATH SOC, V364, P961

[10] Uniform Holder estimate for singularly perturbed parabolic systems of Bose-Einstein condensates and competing species [J].

Dancer, E. N. ;

Wang, Kelei ;

Zhang, Zhitao .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 251 (10) :2737-2769

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