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Evolution Equations and Control Theory (EECT)
 

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

Pages: 599 - 620, Volume 2, Issue 4, December 2013      doi:10.3934/eect.2013.2.599

 
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Wei Deng - Department of Mathematics, Michigan State University, East Lansing, MI 48824, United States (email)
Baisheng Yan - Department of Mathematics, Michigan State University, 619 Red Cedar Road, East Lansing, MI 48824, United States (email)

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.

Keywords:  Landau-Lifshitz equation, no-exchange energy model, existence, stability, regularity, energy identity, asymptotics.
Mathematics Subject Classification:  Primary: 35M31, 35Q60; Secondary: 78A25, 82D40.

Received: September 2012;      Revised: February 2013;      Available Online: November 2013.

 References