American Institute of Mathematical Sciences

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October  2007, 17(4): 867-890. doi: 10.3934/dcds.2007.17.867

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

Shijin Ding 1, , Boling Guo 2, , Junyu Lin 3, and  Ming Zeng 4,

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, China
4. 

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

Received  December 2005 Revised  November 2006 Published  January 2007

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: 35Q8.
Citation: Shijin Ding, Boling Guo, Junyu Lin, Ming Zeng. Global existence of weak solutions for Landau-Lifshitz-Maxwell equations. Discrete & Continuous Dynamical Systems, 2007, 17 (4) : 867-890. doi: 10.3934/dcds.2007.17.867
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