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On two classes of generalized viscous Cahn-Hilliard equations
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 |
$\frac{\partial}{\partial t}[\mu(x,|\mathbf H|)\mathbf H]+ \nabla\times [r(x,t) \nabla \times \mathbf H]=\mathbf F(x,t),$
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.
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