  We prove existence of solution of a $p$-curl type evolutionary system arising
in electromagnetism with a power nonlinearity of order $p$, $1<p<\infty$,
assuming natural tangential boundary conditions. We consider also the
asymptotic behaviour in the power obtaining, when $p$ tends to infinity, a
variational inequality with a curl constraint. We also discuss the existence,
uniqueness and continuous dependence on the data of the solutions to general
variational inequalities with curl constraints dependent on time, as well as
the asymptotic stabilization in time towards the stationary solution with and
without constraint.
