Well-posedness for a general class of quasilinear evolution equations - with applications to Maxwell's equations

Our objective is to undertake a first step towards a systematic investigation of the well-posedness for a wide class of nonlinear Maxwell equations. Our tool of choice is an approach outlined by Tosio Kato (1975) for the analysis of quasi- linear evolution equations using operator semigroups. We will prove an abstract result, that can be applied to both, a wide class of non- linear Maxwell equations, as well as to their corresponding quasilinear wave equations.