# American Institute of Mathematical Sciences

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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