The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps
type: Item
instance of: scholarly article
title: The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps
zbMATH Open document ID: 0798.35139
DOI: 10.1007/BF01191298
author: Min-Chun Hong
author: Boling Guo
published in: Calculus of Variations and Partial Differential Equations
publication date: 1994-03-07T00:00:00Z
review text: Let \(M\) be a Riemannian manifold without boundary and \(N\) be \(S^ 2\). The aim of the paper is to solve the Landau-Lifshitz (LL) type equations of \(M\) into \(S^ 2\): \[ \partial_ t u= -\alpha_ 1 u(u\Delta_ M u)+ \alpha_ 2 u\Delta_ M u, \] \((\alpha_ 1>0\), \(\alpha_ 2=\text{const})\). A global existence of solutions for the LL-equation is proved and some new links between harmonic maps and the solutions of the LL-equation of the ferromagnetic spin chain are established.
Mathematics Subject Classification ID: 35Q58
Mathematics Subject Classification ID: 58E20
Mathematics Subject Classification ID: 58Z05
zbMATH DE Number: 509960
zbMATH Keywords: Landau-Lifshitz equation
zbMATH Keywords: ferromagnetic spin chain
zbMATH Keywords: global existence
Wikidata QID: Q115393941
reviewed by: A. V. Aminova
MaRDI profile type: Publication
cites work: Quasilinear parabolic systems under nonlinear boundary conditions
cites work: Heat flow and boundary value problem for harmonic maps
cites work: The weak solutions to the evolution problems of harmonic maps
cites work: Blow-up and global existence for heat flows of harmonic maps
cites work: Existence and partial regularity results for the heat flow for harmonic maps
cites work: Nonuniqueness for the heat flow of harmonic maps
cites work: Q4729049
cites work: Another Report on Harmonic Maps
cites work: Harmonic Mappings of Riemannian Manifolds
cites work: Q5630031
cites work: Harmonic maps of manifolds with boundary
cites work: Q5759616
cites work: On the evolution of harmonic mappings of Riemannian surfaces
cites work: On the evolution of harmonic maps in higher dimensions
cites work: Q3803566
cites work: Existence and uniqueness of smooth solution for system of ferromagnetic chain
full work available at URL: https://doi.org/10.1007/bf01191298
OpenAlex ID: W2027043390
Recommended article: Q4037777
Recommended article: Q4349571
Recommended article: The Landau--Lifshitz Equation of the Ferromagnetic Spin Chain and Oseen--Frank Flow
Recommended article: Q4367473
Recommended article: Q4388284
Recommended article: Q4392110
Recommended article: Q4352857
Recommended article: Generalized Landau-Lifshitz systems and harmonic maps
Recommended article: Hamiltonian formalism of the Landau-Lifschitz equation for a spin chain with an easy plane
Recommended article: Hamiltonian formalism of the Landau-Lifschitz equation for a spin chain with full anisotropy
description: scientific article; zbMATH DE number 509960