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

Shijin Ding | Zendy; Boling Guo | Zendy; Junyu Lin | Zendy; M. Zeng | Zendy

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

Author(s) -

Shijin Ding,

Boling Guo,

Junyu Lin,

M. Zeng

Publication year - 2007

Publication title -

discrete and continuous dynamical systems

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.289

H-Index - 70

eISSN - 1553-5231

pISSN - 1078-0947

DOI - 10.3934/dcds.2007.17.867

Subject(s) - maxwell's equations , physics , magnetization , magnetic field , maxwell relations , landau–lifshitz–gilbert equation , displacement current , electric displacement field , electric field , constant (computer programming) , mathematical physics , mathematical analysis , classical mechanics , mathematics , inhomogeneous electromagnetic wave equation , optical field , quantum mechanics , computer science , programming language

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.

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