On the quasi-stationary Maxwell equations with monotone characteristics in a multiply connected domain

The quasi-stationary Maxwell equations for a magnetic core with a non-linear characteristic and homeomorphic to a three dimensional torus are reduced to a unique evolution equation involving a monotone operator. This reduction is based on the properties of some functional spaces suited to the study of the operators "curl" and "div," with different kinds of boundary and period conditions. Some existence, uniqueness and regularity results are proved.