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Discrete and Continuous Dynamical Systems - Series A (DCDS-A)
 

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

Pages: 867 - 890, Volume 17, Issue 4, April 2007      doi:10.3934/dcds.2007.17.867

 
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Shijin Ding - Department of Mathematics, South China Normal University, Guangzhou, Guangdong 510631, China (email)
Boling Guo - Institute of Applied Physics & Computational Math., Beijing 100088, China (email)
Junyu Lin - School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong 510631, China (email)
Ming Zeng - College of Applied Sciences, Beijing University of Technology, PingLeYuan100, Chaoyang District, Beijing 100022, China (email)

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.

Keywords:  Landau-Lifshitz-Maxwell equations, global weak solution, existence.
Mathematics Subject Classification:  Primary: 35D10 ; Secondary: 35Q80.

Received: December 2005;      Revised: November 2006;      Available Online: January 2007.