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DOI: 10.5445/IR/1000087659
Veröffentlicht am 20.11.2018

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.

Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
URN: 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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