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Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions

Schnaubelt, Roland; Spitz, Martin

In this article we provide a local wellposedness theory for quasilinear Maxwell equations with absorbing boundary conditions in H m for m ≥ 3. The Maxwell equations are equipped with instantaneous nonlinear material laws leading to a quasilinear symmetric hyperbolic first order system. We consider both linear and nonlinear absorbing boundary conditions. We show existence and uniqueness of a local solution, provide a blow-up criterion in the Lipschitz norm, and prove the continuous dependence on the data. In the case of nonlinear boundary conditions we need a smallness assumption on the tangential trace of the solution. The proof is based on detailed apriori estimates and the regularity theory for the corresponding linear problem which we also develop here.

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DOI: 10.5445/IR/1000088564
Veröffentlicht am 17.12.2018
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: 1000088564
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 45 S.
Serie KIT, Karlsruhe ; 2018/46
Projektinformation SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)
Schlagwörter nonlinear Maxwell system, absorbing or impedance boundary conditions, local wellposedness, blow-up criterion, continuous dependence
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