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Local Wellposedness of Nonlinear Maxwell Equations

Spitz, Martin

Abstract (englisch):

In this work we establish a local wellposedness theory of macroscopic Maxwell equations with instantaneous material laws on domains with perfectly conducting boundary. These equations give rise to a quasilinear initial boundary value problem with characteristic boundary. We provide a priori estimates and a differentiability theorem in arbitrary regularity for the corresponding linear nonautonomous hyperbolic system of partial differential equations. A fixed point argument then yields a unique solution of the nonlinear problem in $H^m$ with $m \geq 3$. We further show a blow-up criterion in the Lipschitz-norm and the continuous dependance on the data.

Volltext §
DOI: 10.5445/IR/1000078030
Veröffentlicht am 18.12.2017
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Hochschulschrift
Publikationsjahr 2017
Sprache Englisch
Identifikator urn:nbn:de:swb:90-780302
KITopen-ID: 1000078030
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 219 S.
Art der Arbeit Dissertation
Fakultät Fakultät für Mathematik (MATH)
Institut Institut für Analysis (IANA)
Prüfungsdatum 26.07.2017
Projektinformation SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015)
Schlagwörter nonlinear Maxwell equations, perfectly conducting boundary conditions, quasilinear initial boundary value problem, characteristic boundary, local wellposedness, hyperbolic system, a priori estimates, regularity theory, blow-up criterion, continuous dependance
Referent/Betreuer Schnaubelt, R.
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