# Local wellposedness of nonlinear Maxwell equations with perfectly conducting boundary conditions

Spitz, Martin

Abstract:
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.

 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:90-826960 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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