# Local wellposedness of quasilinear Maxwell equations with conservative interface conditions

Schnaubelt, Roland; Spitz, Martin

Abstract:
We establish a comprehensive local wellposedness theory for the quasilinear Maxwell system with interfaces in the space of piecewise H$^{m}$-
functions for $m$ $\geq\$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.

 Zugehörige Institution(en) am KIT Institut für Analysis (IANA)Sonderforschungsbereich 1173 (SFB 1173) Publikationstyp Forschungsbericht Jahr 2018 Sprache Englisch Identifikator ISSN: 2365-662X urn:nbn:de:swb:90-876598 KITopen-ID: 1000087659 Verlag KIT, Karlsruhe Umfang 47 S. Serie CRC 1173 ; 2018/35 Schlagworte nonlinear Maxwell system, local wellposedness, perfectly conducting boundary/interface conditions, blow-up criterion, continuous dependence, piecewise regular
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