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In this article we provide a local wellposedness theory for quasilinearMaxwell equations with absorbing boundary conditions in $\mathcal{H}^m$ for $m\geq 3$. The Maxwell equations are equipped with instantaneous nonlinearmaterial laws leading to a quasilinear symmetric hyperbolic first order system.We consider both linear and nonlinear absorbing boundary conditions. We showexistence and uniqueness of a local solution, provide a blow-up criterion inthe Lipschitz norm, and prove the continuous dependence on the data. In thecase of nonlinear boundary conditions we need a smallness assumption on thetangential trace of the solution. The proof is based on detailed aprioriestimates and the regularity theory for the corresponding linear problem whichwe also develop here.

Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions