具有二阶逼近效应场多维Landau-Lifshitz方程解的极限行为  

Limiting behavior of solutions to multidimensional LandauLifshitz equations with second approximation of effective field

作　　者：杨干山[1,2] 吴继晖[3] 郭柏灵[4] 

机构地区：[1]云南民族大学数学系,昆明650031 [2]云南师范大学数学科学研究所,昆明650092 [3]淮南师范学院数学系,淮南232038 [4]北京应用物理与计算数学研究所非线性研究中心,北京100088

出　　处：《中国科学：数学》2013年第5期445-476,共32页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11161057,11101356和11261049);安徽省高校省级科学研究项目(批准号:KJ2011Z345)资助项目

摘　　要：本文给出在Rn+1到S2整体光滑映射控制下的极大值原理,通过这个原理建立具有二阶逼近效应场多维Landau-Lifshitz方程的δ-黏性上解和δ-黏性下解.利用这些δ-黏性上下解,我们建立具有二阶逼近效应场多维Landau-Lifshitz方程的黏性解并获得解的极限行为,即存在两个不相交的开子集M和N使得δ-黏性上解和δ-黏性下解分别在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).In this paper, by a maximum principle under global control map from R^n＋1 to S2, 5-viscosity supersolution and subsolution to multidimensional Landau-Lifshitz equations with the second approximation of effective field are constructed. Utilizing the δ-viscosity supersolution and subsolution, the viscosity solution to the equations is showed and the limiting behavior of the solution to the equations is obtained. Exactly, there exist two disjoint open subsets such that the solutions tend to the point （0 one of them and tend to the point （0,-1, 0） on arbitrary compact subsets 1, O） on arbitrary compact subsets in in the other of them, respectively.

关 键 词：多维Landau-Lifshitz方程 δ-黏性上解 交换场的二阶展开 整体控制映射 极限行为 

分 类 号：O175[理学—数学]