  Maxwell's equations are considered in metric-free form, with a local but
otherwise arbitrary constitutive law. After splitting Maxwell's equations into
evolution equations and constraints, we derive the characteristic equation and
we discuss its properties in detail. We present several results that are
relevant for the question of whether the evolution equations are hyperbolic,
strongly hyperbolic or symmmetric hyperbolic. In particular, we give a
convenient characterisation of all constitutive laws for which the evolution
equations are symmetric hyperbolic. The latter property is sufficient, but not
necessary, for well-posedness of the initial-value problem. By way of example,
we illustrate our results with the constitutive laws of biisotropic media and
of Born-Infeld theory.
