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Local wellposedness of quasilinear Maxwell equations with conservative interface conditions

Schnaubelt, Roland; Spitz, Martin


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.

Volltext §
DOI: 10.5445/IR/1000087659
Veröffentlicht am 20.11.2018
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsjahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000087659
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 47 S.
Serie CRC 1173 ; 2018/35
Schlagwörter nonlinear Maxwell system, local wellposedness, perfectly conducting boundary/interface conditions, blow-up criterion, continuous dependence, piecewise regular
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