| Abstract: |
| The Maxwell equation $u_t +\nabla \times (\rho\; \text{curl}\, u) = f$ is well known as a fundamental equation,
where $u$ is a magnetic field, $\rho$ is a nonnegative function of resistivity and $f$ is a given
vector field. In this context, $ \text{curl}\, u$ stands for the current density, In some situations, it cannot exceed some critical valuue, which may depend on the temperature or the magnetic field $u$. THis leads to a quasi-variational inequalty form of the Maxwell equation, which should also allow us to treat the superconductivity case, when the resistivity $\rho$ drops near zero at some critical temperature. |
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