多维Landau-Lifshitz方程的δ-黏性解  

δ-Viscosity Solution of Multidimensional Landau-Lifshitz Equation

作　　者：郭柏灵[1] 杨干山[2] 

机构地区：[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

出　　处：《数学学报（中文版）》2006年第4期721-736,共16页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10471147;10471046)

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)．The purpose of this paper is to introduce the concepts of S-viscosity supersolution, δ-viscosity subsolution and δ-viscosity solution, and give their properties, and using these properties prove the existence of δ-viscosity supersolution and δ-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 the δ-viscosity supersolution and δ-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.

关 键 词：多维Landau-Lifshitz方程 δ-黏性上(下)解 平均曲率 

分 类 号：O175[理学—数学]