On Landau-Lifshitz equations  of  no-exchange energy  models in ferromagnetics

Wei Deng; Baisheng Yan

doi:10.3934/eect.2013.2.599

Article Contents

2013, Volume 2, Issue 4: 599-620. Doi: 10.3934/eect.2013.2.599

This issue Previous Article Fluid-structure interaction with and without internal dissipation of the structure: A contrast study in stability Next Article A remark on Littman's method of boundary controllability

On Landau-Lifshitz equations of no-exchange energy models in ferromagnetics

Wei Deng^1, and
Baisheng Yan^2,

1.
Department of Mathematics, Michigan State University, East Lansing, MI 48824
2.
Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, MI 48824

Received: September 2012

Revised: February 2013

Published: December 2013

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Abstract

In this paper, we study Landau-Lifshitz equations of ferromagnetism with a total energy that does not include a so-called exchange energy. Many problems, including existence, stability, regularity and asymptotic behaviors, have been extensively studied for such equations of models with the exchange energy. The problems turn out quite different and challenging for Landau-Lifshitz equations of no-exchange energy models because the usual methods based on certain compactness do not apply. We present a new method for the existence of global weak solution to the Landau-Lifshitz equation of no-exchange energy models based on the existence of regular solutions for smooth data and certain stability of the solutions. We also study higher time regularity, energy identity and asymptotic behaviors in some special cases for weak solutions.

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Mathematics Subject Classification: Primary: 35M31, 35Q60; Secondary: 78A25, 82D40.

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