| 多维Landau-Lifshitz方程的δ-黏性解 |
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| 引用本文： | 郭柏灵,杨干山.多维Landau-Lifshitz方程的δ-黏性解[J].数学学报,2006,49(4):721-736. |
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| 作者姓名： | 郭柏灵 杨干山 |
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| 作者单位： | [1]北京应用物理与计算数学研究所非线性研究中心,北京100088 [2]云南民族大学数学系,昆明650031 |
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| 基金项目： | 国家自然科学基金资助项目（10471147;10471046）;致谢 感谢审稿人为我们提出了很好的建议! |
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| 摘 要： | 本文引入δ-黏性上解,δ-黏性下解和δ-黏性解的概念,给出一些相关性质,利用这些性质证明取值于三维单位球面的多维Landau-Lifshitz方程的δ-黏性上解和δ-黏性下解的存在性,揭示存在两个不相交的开子集M和N,使得δ-黏性上解和δ-黏性下解在M内任一紧子集上趋于(0,1,0),在N内任一紧子集上趋于(0,-1,0)．
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| 关 键 词： | 多维Landau-Lifshitz方程 δ-黏性上(下)解 平均曲率 |
| 文章编号： | 0583-1431（2006）04-0721-16 |
| 收稿时间： | 2002-12-20 |
| 修稿时间： | 2002-12-202005-12-20 |
δ-Viscosity Solution of Multidimensional Landau-Lifshitz Equation |
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| Bo Ling GUO,Gan Shan YANG.δ-Viscosity Solution of Multidimensional Landau-Lifshitz Equation[J].Acta Mathematica Sinica,2006,49(4):721-736. |
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| Authors: | Bo Ling GUO Gan Shan YANG |
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| Institution: | Center for Nonlinear Studies, Institute of Applied Physics and Computational Mathematics Beijing 100088, P. R. China;Department of Mathematics, Yunnan Nationality Institute, Kunming 650031, P. R. China |
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| Abstract: | The purpose of this paper is to introduce the concepts ofδ-viscosity supersolution,δ-viscosity subsolution andδ-viscosity solution, and give their properties, and using these properties prove the existence ofδ-viscosity supersolution andδ-viscosity subsolution of the multidimensional Landau-Lifshitz equation with values in a unit sphere, and indicate that there exist two disjoint open subsets M and N such that theδ-viscosity supersolution andδ-viscosity subsolution tend to (0,1,0) on arbitrary compact sets in M, and tend to (0,-1,0) on arbitrary compact sets in N. |
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| Keywords: | multidimensional Landau-Lifshitz equation δ-viscosity supersolution (subsolution) mean curvature |
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