American Institute of Mathematical Sciences

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July  2010, 14(1): 199-207. doi: 10.3934/dcdsb.2010.14.199

Global weak solutions to the 1-D fractional Landau-Lifshitz equation

Xueke Pu 1, , Boling Guo 2, and  Jingjun Zhang 3,

1. 

College of Mathematics and Physics, Chongqing University, Chongqing 400044, China
2. 

Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, China
3. 

College of Mathematics and Information Engineering, Jiaxing University, Zhejiang, 314001, China

Received  June 2009 Revised  February 2010 Published  April 2010

In this work, we generalize the idea of Ginzburg-Landau approximation to study the existence and asymptotic behaviors of global weak solutions to the one dimensional periodical fractional Landau-Lifshitz equation modeling the soft micromagnetic materials. We apply the Galerkin method to get an approximate solution and, to get the convergence of the nonlinear terms we introduce the commutator structure and take advantage of special structures of the equation.
Keywords: Heat flow of harmonic maps, Commutator estimate., Fractional Landau-Lifshitz equation, Ginzburg-Landau approximation.
Mathematics Subject Classification: Primary: 35Qxx, 58E20; Secondary: 82Dx.
Citation: Xueke Pu, Boling Guo, Jingjun Zhang. Global weak solutions to the 1-D fractional Landau-Lifshitz equation. Discrete and Continuous Dynamical Systems - B, 2010, 14 (1) : 199-207. doi: 10.3934/dcdsb.2010.14.199
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