具有二阶逼近效应场多维Landau-Lifshitz 方程解的极限行为

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).

Limiting behavior of solutions to multidimensional Landau-Lifshitz equations with second approximation of effective field

In this paper, by a maximum principle under global control map from Rⁿ⁺¹ to S², δ-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, 1, 0) on arbitrary compact subsets in one of them and tend to the point (0, -1, 0) on arbitrary compact subsets in the other of them, respectively.