Asymptotic behaviors of governing equation of gauged sigma model for Heisenberg ferromagnet

Huyuan Chen; Feng Zhou

doi:10.1016/j.na.2020.111788

Asymptotic behaviors of governing equation of gauged sigma model for Heisenberg ferromagnet

Huyuan Chen^*
, Feng Zhou

^*Corresponding author for this work

School of Mathematical Sciences

Jiangxi Normal University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this note, we study weak solutions of equation [Formula presented] where {δ_{p_i}}_i=1 ^N (resp. {δ_{q_j}}_j=1 ^M ) are Dirac masses concentrated at the points p_i,i=1,…,N, (resp. q_j,j=1,…,M) and N−M>1. Eq. (0.1) represents a governing equation of gauged sigma model for Heisenberg ferromagnet. We show that it has a sequence of solutions u_β having behaviors as −βln|x|+O(1) at infinity with a free parameter β∈(2,2(N−M)), and our concern in this paper is to study the asymptotic behavior of b_β as β approaching the extremal values 2 and 2(N−M).

Original language	English
Article number	111788
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	196
DOIs	https://doi.org/10.1016/j.na.2020.111788
State	Published - Jul 2020

Keywords

Asymptotic behavior
Dirac mass
Gauged sigma model

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10.1016/j.na.2020.111788

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title = "Asymptotic behaviors of governing equation of gauged sigma model for Heisenberg ferromagnet",

abstract = "In this note, we study weak solutions of equation [Formula presented] where \{δpi \}i=1 N (resp. \{δqj \}j=1 M ) are Dirac masses concentrated at the points pi,i=1,…,N, (resp. qj,j=1,…,M) and N−M>1. Eq. (0.1) represents a governing equation of gauged sigma model for Heisenberg ferromagnet. We show that it has a sequence of solutions uβ having behaviors as −βln|x|+O(1) at infinity with a free parameter β∈(2,2(N−M)), and our concern in this paper is to study the asymptotic behavior of bβ as β approaching the extremal values 2 and 2(N−M).",

keywords = "Asymptotic behavior, Dirac mass, Gauged sigma model",

author = "Huyuan Chen and Feng Zhou",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Ltd",

year = "2020",

month = jul,

doi = "10.1016/j.na.2020.111788",

language = "英语",

volume = "196",

journal = "Nonlinear Analysis, Theory, Methods and Applications",

issn = "0362-546X",

publisher = "Elsevier Ltd",

}

TY - JOUR

T1 - Asymptotic behaviors of governing equation of gauged sigma model for Heisenberg ferromagnet

AU - Chen, Huyuan

AU - Zhou, Feng

PY - 2020/7

Y1 - 2020/7

N2 - In this note, we study weak solutions of equation [Formula presented] where {δpi }i=1 N (resp. {δqj }j=1 M ) are Dirac masses concentrated at the points pi,i=1,…,N, (resp. qj,j=1,…,M) and N−M>1. Eq. (0.1) represents a governing equation of gauged sigma model for Heisenberg ferromagnet. We show that it has a sequence of solutions uβ having behaviors as −βln|x|+O(1) at infinity with a free parameter β∈(2,2(N−M)), and our concern in this paper is to study the asymptotic behavior of bβ as β approaching the extremal values 2 and 2(N−M).

AB - In this note, we study weak solutions of equation [Formula presented] where {δpi }i=1 N (resp. {δqj }j=1 M ) are Dirac masses concentrated at the points pi,i=1,…,N, (resp. qj,j=1,…,M) and N−M>1. Eq. (0.1) represents a governing equation of gauged sigma model for Heisenberg ferromagnet. We show that it has a sequence of solutions uβ having behaviors as −βln|x|+O(1) at infinity with a free parameter β∈(2,2(N−M)), and our concern in this paper is to study the asymptotic behavior of bβ as β approaching the extremal values 2 and 2(N−M).

KW - Asymptotic behavior

KW - Dirac mass

KW - Gauged sigma model

UR - https://www.scopus.com/pages/publications/85079278357

U2 - 10.1016/j.na.2020.111788

DO - 10.1016/j.na.2020.111788

M3 - 文章

AN - SCOPUS:85079278357

SN - 0362-546X

VL - 196

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

M1 - 111788

ER -

Asymptotic behaviors of governing equation of gauged sigma model for Heisenberg ferromagnet

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