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R^3中各向异性Landau-Lifshitz方程的部分正则解 被引量：3

Partially Regular Solutions to the Anisotropic Landau-Lifshitz Equation in (?)~3
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摘要 证明了当三维空间中各向异性Landau-Lifshitz方程的弱解满足稳定性条件时,其解具有部分正则性,并且对易面类型的方程,利用Ginzburg-Landau逼近构造了一个整体的部分正则解。 This paper establishes a partial regularity result under the stability condition for weak solutions to the anisotropic Landau-Lifshitz equation in three space dimensions. Moreover, using the Ginzburg-Landau approximation, the authors construct a globally partially regular solution in the easy-plane case.
作者 方道元 李太龙
机构地区 浙江大学数学系
出处 《数学年刊（A辑）》 CSCD 北大核心 2007年第4期449-466,共18页 Chinese Annals of Mathematics
基金 国家自然科学基金(No.10271108 No.10571158)资助的项目。
关键词 各向异性Landau-Lifshitz方程 部分正则性 存在性 Anisotropic Landau-Lifshitz equation, Partial regularity, Existence
分类号 O175.2 [理学—基础数学]
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参考文献20

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同被引文献23

  • 1Bo Ling GUO,Gan Shan YANG.Existence and Stability of Static Solutions of the Landau-Lifshitz Equation with Multi-direct Effective Field[J].Acta Mathematica Sinica,English Series,2004,20(6):1135-1152. 被引量：5
  • 2郭柏灵,王友德.广义Landau-Lifshitz方程组和调和映射[J].中国科学（A辑）,1996,26(9):799-810. 被引量：1
  • 3Landau L, Lifshitz E. On the theory of the dispersion of magnetic permeability in ferromagnetic bodies. Phy Z Sowjet, 8:153-169 (1935)
  • 4Lakshmanana M, Naksmurs K. Landau-Lifshitz equations of ferro-magnetism: Exact treatment of the Gilbert damping. Phys Rev Lett, 53(6): 2497-2499 (1984)
  • 5Alouges F, Soyeur A. On global weak solutions for Landau-Lifshitz equations: existence and nonuniqueness. Nonlinear Anal, 18(11): 1071-1084 (1992)
  • 6Guo B L, Hong M C. The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps. Calc Vat Partial Differential Equation, 1(3): 311-334 (1993)
  • 7Melcher C. Existence of partially regular solutions for Landau-Lifshitz equations in R^3. Comm Partial Differential Equation, 30(4-6): 567-587 (2005)
  • 8Wang C Y. On Landau-Lifshitz equation in dimensions at most four. Indian Univ Math J, 55(5): 1615-1644 (2006)
  • 9Moser R. Partial regularity for the Landau-Lifshitz equation in small dimensions. Max-Planck-Institute for Mathematics in the Science. Preprint, 2002
  • 10Liu X G. Partial regularity for the Landau-Lifshitz system. Calc Vat Partial Differential Equation, 20(2): 157-173 (2004)

引证文献3

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数学年刊（A辑）
2007年 第4期

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