Some remarks on the structure of finite Morse index solutions to the Allen-Cahn equation in R2

被引：0
|
作者：
Wang, Kelei [1 ]
机构：
[1] Wuhan Univ, Sch Math & Stat & Computat Sci, Hubei Key Lab, Wuhan 430072, Hubei, Peoples R China
来源：
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2017年 / 24卷 / 05期
关键词：
Finite Morse index solution; Phase transition; Allen-Cahn; Minimal surface; PLANE; SPACE;
D O I：
10.1007/s00030-017-0481-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
For a solution of the Allen-Cahn equation in R-2, under the natural linear growth energy bound, we show that the blowing down limit is unique. Furthermore, if the solution has finite Morse index, the blowing down limit satisfies the multiplicity one property.
引用
收藏
页数：17
相关论文
共 50 条
  • [1] AXIALLY SYMMETRIC SOLUTIONS OF THE ALLEN-CAHN EQUATION WITH FINITE MORSE INDEX
    Gui, Changfeng
    Wang, Kelei
    Wei, Jucheng
    [J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 373 (05) : 3649 - 3668
  • [2] Morse index of layered solutions to the heterogeneous Allen-Cahn equation
    Du, Yihong
    Nakashima, Kimie
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 238 (01) : 87 - 117
  • [3] Multiple-end solutions to the Allen-Cahn equation in R2
    del Pino, Manuel
    Kowalczyk, Michal
    Pacard, Frank
    Wei, Juncheng
    [J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 258 (02) : 458 - 503
  • [4] Symmetry of Traveling Wave Solutions to the Allen-Cahn Equation in R2
    Gui, Changfeng
    [J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2012, 203 (03) : 1037 - 1065
  • [5] On the existence and Morse index of solutions to the Allen-Cahn equation in two dimensions
    Kowalczyk, Michal
    [J]. ANNALI DI MATEMATICA PURA ED APPLICATA, 2005, 184 (01) : 17 - 52
  • [6] On the existence and Morse index of solutions to the Allen-Cahn equation in two dimensions
    Michał Kowalczyk
    [J]. Annali di Matematica Pura ed Applicata, 2005, 184 : 17 - 52
  • [7] A two end family of solutions for the inhomogeneous Allen-Cahn equation in R2
    Zuniga, Andres
    Agudelo, Oscar
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (01) : 157 - 205
  • [8] Entire solutions in R2 for a class of Allen-Cahn equations
    Alessio, F
    Montecchiari, P
    [J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2005, 11 (04): : 633 - 672
  • [9] ON THE ASYMPTOTIC BEHAVIOR OF SYMMETRIC SOLUTIONS OF THE ALLEN-CAHN EQUATION IN UNBOUNDED DOMAINS IN R2
    Fusco, Giorgio
    Leonetti, Francesco
    Pignotti, Cristina
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (02): : 725 - 742
  • [10] TOWARDS CLASSIFICATION OF MULTIPLE-END SOLUTIONS TO THE ALLEN-CAHN EQUATION IN R2
    Kowalczyk, Michal
    Liu, Yong
    Pacard, Frank
    [J]. NETWORKS AND HETEROGENEOUS MEDIA, 2012, 7 (04) : 837 - 855
12345