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2007, Volume 17, Issue 4: 867-890. Doi: 10.3934/dcds.2007.17.867
This issue Previous Article The parameterization method for one- dimensional invariant manifolds of higher dimensional parabolic fixed points Next Article The dynamical Borel-Cantelli lemma for interval maps

Global existence of weak solutions for Landau-Lifshitz-Maxwell equations

  • 1.

    Department of Mathematics, South China Normal University, Guangzhou, Guangdong 510631

  • 2.

    Institute of Applied Physics & Computational Math., Beijing 100088

  • 3.

    School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong 510631

  • 4.

    College of Applied Sciences, Beijing University of Technology, PingLeYuan100, Chaoyang District, Beijing 100022

Received:  November 30, 2005
Revised:  October 31, 2006
Published:  September 2007
Abstract Related Papers Cited by
    Abstract
  • In this paper we study the model that the usual Maxwell's equations are supplemented with a constitution relation in which the electric displacement equals a constant time the electric field plus an internal polarization variable and the magnetic displacement equals a constant time the magnetic field plus the microscopic magnetization. Using the Galerkin method and viscosity vanishing approach, we obtain the existence of the global weak solution for the Landau-Lifshitz-Maxwell equations. The main difficulties in this study are due to the loss of compactness in the system.
    Mathematics Subject Classification: Primary: 35D10 ; Secondary: 35Q80.

    Citation:
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