Explicit piecewise smooth solutions of Landau-Lifshitz equation with discontinuous external field |
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| Authors: | Gan-shan Yang Yun-zhang Zhang Li-min Liu |
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| Institution: | (1) Institute of Mathematics Science, Yunnan Normal University, Kunming, 650092, China;(2) Faculty of Science, Xi’an Jiaotong University, Xi’an, 710049, China;(3) College of Mathematics and Physics, Chongqing University, Chongqiong, 400030, China;(4) Department of Mathematics, Yunnan National University, Kunming, 650031, China |
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| Abstract: | 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.
Supported by the National Natural Science Foundation of China (No. 10861014), and The Institute of Mathematical Sciences,
Chinese University of Hongkong. |
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| Keywords: | Multidimensional Landau-Lifshitz equation discontinuous external field piecewise smooth solution |
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