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

Xueke Pu; Boling Guo; Jingjun Zhang

doi:10.3934/dcdsb.2010.14.199

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2010, Volume 14, Issue 1: 199-207. Doi: 10.3934/dcdsb.2010.14.199

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

1.
College of Mathematics and Physics, Chongqing University, Chongqing 400044
2.
Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088
3.
College of Mathematics and Information Engineering, Jiaxing University, Zhejiang, 314001

Received: May 31, 2009

Revised: January 31, 2010

Published: June 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 35Qxx, 58E20; Secondary: 82Dxx.

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