Asymptotic behaviors of governing equation of gauged sigma model for Heisenberg ferromagnet. (July 2020)

• Record Type: Journal Article
• Authors: Chen, Huyuan; Zhou, Feng
• Is Part Of: Nonlinear analysis. Volume 196(2020)
• Publication Date: 2020-07
• Subjects: 35R06 -- 35A01 -- 35J66; Gauged sigma model -- Dirac mass -- Asymptotic behavior; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111788
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this note, we study weak solutions of equation (0.1) Δ u = 4 e u 1 + e u − 4 π ∑ i = 1 N δ p i + 4 π ∑ j = 1 M δ q j in R 2, 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 − β ln | 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 ) .