Local wellposedness of quasilinear Maxwell equations with conservative interface conditions

2018/11/21 by Schnaubelt, Roland, Spitz, Martin
#35L50 #35L60 #35Q61 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.08714

Abstract

We establish a comprehensive local wellposedness theory for the quasilinear Maxwell system with interfaces in the space of piecewise H^m-functions for m ≥ 3. The system is equipped with instantaneous and piecewise regular material laws and perfectly conducting interfaces and boundaries. We also provide a blow-up criterion in the Lipschitz norm and prove the continuous dependence on the data. The proof relies on precise a priori estimates and the regularity theory for the corresponding linear problem also shown here.

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