June  2005, 4(2): 431-444. doi: 10.3934/cpaa.2005.4.431

Global solvability for a singular nonlinear Maxwell's equations

1. 

Department of Mathematics, Guizou University, Guiyang, Guizhou Province, China

2. 

Department of Mathematics, Washington State University, Pullman, WA 99164, United States

Received  June 2004 Revised  September 2004 Published  March 2005

In this paper we study a singular nonlinear evolution system:

$\frac{\partial}{\partial t}[\mu(x,|\mathbf H|)\mathbf H]+ \nabla\times [r(x,t) \nabla \times \mathbf H]=\mathbf F(x,t),$

where $\mathbf H$ represents the magnetic field in a quasi-stationary electromagnetic field and $\mu(x,|\mathbf H|)$ is the magnetic permeability in a conductive medium, which strongly depends on the strength of $\mathbf H$ such as $\mu(x,|\mathbf H|)=|\mathbf H|^b$ with $b>0$. We prove that under appropriate initial and boundary conditions the system has a global weak solution and the solution is also unique.

Citation: W. Wei, H. M. Yin. Global solvability for a singular nonlinear Maxwell's equations. Communications on Pure & Applied Analysis, 2005, 4 (2) : 431-444. doi: 10.3934/cpaa.2005.4.431
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