Explicit Piecewise Smooth Solutions of Landau-Lifshitz Equation with Discontinuous External Field  

作　　者：Gan-shan Yang Yun-zhang Zhang Li-min Liu 

机构地区：[1]Institute of Mathematics Science, Yunnan Normal University, Kunming 650092, China [2]Department of Mathematics, Yunnan National University, Kunming 650031, China [3]Faculty of Science, Xi'an Jiaotong University, Xi'an 710049, China [4]College of Mathematics and Physics, Chongqing University, Chongqiong 400030, China

出　　处：《Acta Mathematicae Applicatae Sinica》2009年第1期61-74,共14页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.10861014);The Institute of Mathematical Sciences,Chinese University of Hongkong.

摘　　要：In this paper, we shall construct some explicit piecewise smooth （global continuous） solutions as well as blow up solutions to the multidimensional Landau-Lifshitz equation, subject to the external magnetic fields being both discontinuous and unbounded. When the external magnetic field is continuous, some explicit exact smooth solutions and blow up solution are also constructed. We also establish some necessary and sufficient conditions to ensure that the solution of multidimensional Landau-Lifshitz equation with external magnetic field converges to the solution of equation without external magnetic field when the external magnetic field tends to zero.In this paper, we shall construct some explicit piecewise smooth （global continuous） solutions as well as blow up solutions to the multidimensional Landau-Lifshitz equation, subject to the external magnetic fields being both discontinuous and unbounded. When the external magnetic field is continuous, some explicit exact smooth solutions and blow up solution are also constructed. We also establish some necessary and sufficient conditions to ensure that the solution of multidimensional Landau-Lifshitz equation with external magnetic field converges to the solution of equation without external magnetic field when the external magnetic field tends to zero.

关 键 词：Multidimensional Landau-Lifshitz equation discontinuous external field piecewise smoothsolution 

分 类 号：O18[理学—数学]