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Local wellposedness of nonlinear Maxwell equations with perfectly conducting boundary conditions

Spitz, Martin

In this article we develop the local wellposedness theory for quasilinear Maxwell equations in H$^{m}$ for all $m \geq \ $3 on domains with perfectly conducting boundary conditions. The macroscopic Maxwell equations with instantaneous material laws for the polarization and the magnetization lead to a quasilinear first order hyperbolic system whose wellposedness in H³ is not covered by the available results in this case. We prove the existence and uniqueness of local solutions in Hm with $m \geq \ $3 of the corresponding initial boundary value problem if the material laws and the data are accordingly regular and compatible. We further characterize finite time blowup in terms of the Lipschitz norm and we show that the solutions depend continuously on their data. Finally, we establish the finite propagation speed of the solutions.

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DOI: 10.5445/IR/1000082696
Veröffentlicht am 11.05.2018
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000082696
Verlag KIT, Karlsruhe
Umfang 46 S.
Serie CRC 1173 ; 2018/7
Schlagworte nonlinear Maxwell equations, perfectly conducting boundary conditions, quasilinear initial boundary value problem, hyperbolic system, local wellposedness, blow-up criterion, continuous dependance
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