Abstract
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.
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